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Let L be the line passing through the point P=(1, −1, −5) with direction vector →d=[−2, −4, 3]T, and let T be the plane defined by −x+y−3z = −1. Find the point Q where L and T intersect.

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  1. mathematics

    Let L1 be the line passing through the point P1=(16, −1, −12) with direction vector →d1=[3, −1, −2]T, and let L2 be the line passing through the point P2=(4, 7, −17) with direction vector →d2=[3, 1, −2]T. Find the shortest distance d

  2. Algebra

    can somebody please help me with this question I've spent more than 3 hours on this, still nothing Let L1 be the line passing through the point P1=(2, −4, −6) with direction vector →d1=[1, 0, 2]T, and let L2 be the line passing through the point

  3. Linear Algebra

    Let L1 be the line passing through the point P1=(9, −1, 15) with direction vector →d1=[−2, −1, −3]T, and let L2 be the line passing through the point P2=(9, 4, 8) with direction vector →d2=[−2, −1, −1]T. Find the shortest distance d

  5. Linear algebra

    Let L1 be the line passing through the point P1=(−1, −1, 8) with direction vector →d1=[1, 0, −3], and let L2 be the line passing through the point P2=(7, −11, 14) with direction vector →d2=[1, 2, −3]. Find the shortest distance d between

  6. linear algebra

    Let L1 be the line passing through the point P1=(9, 0, 0) with direction vector →d1=[3, 2, −2]T, and let L2 be the line passing through the point P2=(−10, 8, 4) with direction vector →d2=[3, 0, 2]T. Find the shortest distance d between these two

  7. algebra

    Let L1 be the line passing through the point P1=(4, 5, −5) with direction vector →d1=[0, −1, 1]T, and let L2 be the line passing through the point P2=(13, 0, 0) with direction vector →d2=[4, −1, 3]T. Find the shortest distance d between these two

  8. Algebra

    Let L1 be the line passing through the points Q1=(−2, −3, −4) and Q2=(−5, −2, −3) and let L2 be the line passing through the point P1=(−27, 31, −25) with direction vector →d=[−6, 9, −6]T. Determine whether L1 and L2 intersect. If so,

  10. math

    Let L1 be the line passing through the points Q1=(−2, −5, 4) and Q2=(4, −1, 2) and let L2 be the line passing through the point P1=(10, 8, −7) with direction vector →d=[1, −1, 2]T. Determine whether L1 and L2 intersect. If so, find the point of

  11. math

    Let L1 be the line passing through the points Q1=(4, −1, −2) and Q2=(1, 0, −1) and let L2 be the line passing through the point P1=(−6, 21, −8) with direction vector →d=[−3, 9, −3]T. Determine whether L1 and L2 intersect. If so, find the

  12. math

    Let L1 be the line passing through the points Q1=(4, −1, −2) and Q2=(1, 0, −1) and let L2 be the line passing through the point P1=(−6, 21, −8) with direction vector →d=[−3, 9, −3]T. Determine whether L1 and L2 intersect. If so, find the

  13. math

    Let L1 be the line passing through the points Q1=(4, 1, 2) and Q2=(0, −1, 4) and let L2 be the line passing through the point P1=(20, 8, −7) with direction vector →d=[−3, −1, 2]T. Determine whether L1 and L2 intersect. If so, find the point of

  15. hch

    Let L1 be the line passing through the points Q1=(2, −2, 5) and Q2=(−4, −6, 3) and let L2 be the line passing through the point P1=(7, 4, 0) with direction vector →d=[−1, −2, 3]T. Determine whether L1 and L2 intersect. If so, find the point of

  16. Algebra

    I spent hours on this and I still cant figure it out please help me: Let L1 be the line passing through the points Q1=(4, 2, −3) and Q2=(5, 5, −5). Find a value of k so the line L2 passing through the point P1 = P1(3, 7, k) with direction vector

  17. linear algebra

    Let L1 be the line passing through the points Q1=(3, −3, 4) and Q2=(−3, 6, 7). Find a value of k so the line L2 passing through the point P1 = P1(−6, 11, k) with direction vector →d=[1, −1, −2]T intersects with L1. Not sure how to go on..

  18. math

    Let L1 be the line passing through the points Q1=(4, 2, −3) and Q2=(0, −2, 3). Find a value of k so the line L2 passing through the point P1 = P1(−11, 2, k) with direction vector →d=[3, −2, −3]T intersects with L1

  20. Vectors

    Determine the vector equation of a line passing through the point P(3,2,-1) and with a direction vector perpendicular to the line r=(2,-3,4)+s(1,1,-2), seR

  21. Precalc

    A line in space has the vector equation shown here. Fill in the blanks to find the position vector to the fixed point on the line that appears in the equation: vector r=(5+(6/11)d)vector i + (3+(9/11)d)vector j + (7+(2/11)d)vector k vector v= _____ vector

  22. Linear algebra

    Let L1 be the line passing through the points Q1=(−2, 1, 1) and Q2=(−4, 4, 0) and let L2 be the line passing through the point P1=(−6, −6, 0) with direction vector →d=[9, 6, 3]T. Determine whether L1 and L2 intersect. If so, find the point of

  23. math

    Let L1 be the line passing through the points Q1=(−1, 5, 3) and Q2=(1, 6, 1) and let L2 be the line passing through the point P1=(3, 10, 2) with direction vector →d=[4, 4, −2]T. Determine whether L1 and L2 intersect. If so, find the point of

  25. Linear Algebra

    Let L1 be the line passing through the points Q1=(−3, −1, 5) and Q2=(−1, −7, −1) and let L2 be the line passing through the point P1=(3, −17, −9) with direction vector →d=[−1, 1, −1]T. Determine whether L1 and L2 intersect. If so, find

  26. linear algebra

    Let L be the line passing through the point P=(−3, −1, −5) with direction vector →d=[4, 0, 4]T, and let T be the plane defined by 4x−y−3z = 16. Find the point Q where L and T intersect. please help..

  27. Algebra

    Let L be the line passing through the point P=(1, −1, −5) with direction vector →d=[−2, −4, 3]T, and let T be the plane defined by −x+y−3z = −1. Find the point Q where L and T intersect.

  28. mathematics! Can Someone Help Me?!!

    Let L be the line passing through the point P=(−4, −3, −5) with direction vector →d=[3, −1, 3]T. Find the shortest distance d from the point P0=(1, −1, −1) to L, and the point Q on L that is closest to P0. Use the square root where needed to

  30. Linear algebra

    Let L be the line passing through the point P(−2, −2, 2) with direction vector d=[1, −2, 3]T. Find the shortest distance d from the point P0(−4, −4, −5) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where

  31. Algebra

    can anybody help me with this question please? Let L be the line passing through the point P=(5, −5, 3) with direction vector →d=[1, −3, −2]T. Find the shortest distance d from the point P0=(−4, −1, 4) to L,

  32. Discrete Math: Equations of Line in a Plane

    I'm stuck on these questions. Can you please show me a step by step solution? 20) For each of the following, find a normal vector, a direction vector, and a point of each line. Note, normal vector means perpendicular to the direction vector. a) 3x - 6y =

  33. Math: Equations of Line in a Plane

    I'm stuck on these questions. Can you please show me a step by step solution? 20) For each of the following, find a normal vector, a direction vector, and a point of each line. Note, normal vector means perpendicular to the direction vector. a) 3x - 6y =

  35. Maths Vector Helpppp

    The points A and B have position vectors, relative to the origin O, given by −−→OA = i+2j+3k and −−→OB = 2i+j+3k. The line l has vector equation r = (1−2t)i+ (5+t)j+ (2−t)k. (i) Show that l does not intersect the line passing through A and

  36. calculus

    Find a unit vector U such that the rate of change of f in the direction of U at the given point is maximum. point being (3,5,pi) I know hos to do this when given a direction but since im asked to ind the unit vector first it kinda throws me off. do i just

  37. mathematics, calculus

    Determine vector and parametric equations for the line through the point A(2, 5) with direction vector Vector m = (1, -3).

  38. Calc. for Reiny

    this can be done by projections of two vector. recall that the scalar projection of vector b on vector a is a∙b/│a│ so let's find a point on the give line, e.g. the point B(6,0,1) (I let t=0) draw a perpendicular from your given point P(1,-5,2) to

  40. gen. physics II

    Two charges, +Q and ‑Q, are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated. Which vector best represents the direction of the electric field at that point? a. Vector EA b. Vector EB C.

  41. Maths

    find the vector equation of line passing through the point 2,0,0 and parallel to line r=lambda k

  42. Calculus

    A line has Cartesian equation 3x-2y+3=0 .Determine a direction vector for a line that is parallel to this line. Could someone explain to me why the answer is direction vector: d=(2,3)

  43. Calculus

    Determine vector and parametric equations for the line through the point A(2, 5) with direction vector m = (1, -3).

  45. math

    let L1 be the line throught (1,-6,2) with direction vector (1,2,1) and L2 be the line throught (0,4,1) with direction vector (2,1,2).Detrmine Whether trh lines are parallel,intersec or skew.if intersec,find the point of intersec

  46. Math

    Would the vector equation of a line through the point (2,5) with direction vector v = (3, 2) be (2, 5) + t(3, 2)?

  47. Physical Science

    1. Which quantity is scalar? momentum energy*** force velocity 2. Which option describes a vector quantity?(1 point) It has magnitude, units, and direction.*** It has magnitude, but no units or direction. It has no magnitude, units, or direction. It has

  48. Math/Vectors

    I need help on a homework problem. "Determine a vector equation for the line perpendicular to 4x-3y=17 and through point (-2,4). The answer in the book is given as [x,y]=[-2,4]+t[-4,3].Isn't the normal to the scalar equation [4,-3] and wouldn't this be the

  50. Physics

    1. Consider the two vectors P and Q. The definition of P is P = 􀀃i × (􀀃i × 􀀃j). The definition of Q is Q = (􀀃i × 􀀃i) × 􀀃j . a. The magnitude of P is equal to the magnitude of Q. b. The magnitude of P is greater than the magnitude of

  51. Physics

    The center of mass of the arm shown in the figure is at point A. Find the magnitudes (in N) of the tension force Ft and the force Fs which hold the arm in equilibrium. (Let 𝜃 = 23.5°.) Assume the weight of the arm is 48.7 N. An arm is extending

  52. Physics

    A person walks in the following pattern: 2.8 km north, then 2.7 km west, and finally 6.9 km south. Construct the vector diagram that represents this motion and from it judge how far and in what direction a bird would fly in a straight line from the same

  53. Vectors

    A person walks in the following pattern: 4.8 km north, then 1.3 km west, and finally 1.5 km south. Construct the vector diagram that represents this motion and from it judge how far and in what direction a bird would fly in a straight line from the same

  55. math

    Previously you found that a 15-degree counterclockwise rotation centered at(2,1)sends the point(4,6)to another point (x, y) ≈ (2.638, 6.347). The diagram on the right shows the vector v in the same direction as vector [2,5], only with a different length.

  56. Vectors

    Determine the vector equation of a plane that contains the line with symmetric equation (x+3)/-2=(y+1)/5=(z+2)/4 and the point P(1,3,0). For this question to find the direction vector you would use subtraction with the points (-3,-1,-2) and (1,3,0). Why

  57. maths

    Let L be the line through the point Q = (−1, 11, 11) and direction vector →d=[−1, 2, 2]T. Find the two distinct points R1 and R2 on L at distance 3√10 to the point P = (1, 4, 1). R1 = (0, 0, 0) R2 = (0, 0, 0)

  58. Linear Algebra

    2 people move in the same direction along a line of equation: (x + 3)/10 = (y + 10)/20 = (z - 10)/-20 Mobile M1 is at a point A(-3, -10, 10) and moves at a velocity of 6m/s towards point B(7, 10, -10) where Mobile 2 is found, walking in the same direction

  60. physics

    A roller coaster moves 85 m horizontally, then travels 45 m at an angle of 30.0 degrees above the horizontal. What is its displacement from its starting point? Use graphical techniques. How would I solve this? Solve it my adding the vector displacement of

  61. Calculus

    Determine the equation of the line described by the given information. a) slope -2/3, passing through (0,6) b) passing through points (2,7) and (6,11) c) parallel to y=4x-6 passing through point (2,6)

  62. maths

    The position vector of m in the same plane are as the point a and b is given by m=1÷2(a+b).if the vector A(-4,-3),B(2,-1).What is the direction and the relationship of vector AM and vector BM

  63. Math

    A straight line l is parallel to a vector a and passes through a point B whose position vector is b. The point C has position vector c and vectoe p os the position vector of the foot of the perpendicular drawn from C to l. Prove that p = [ (c-b)a ]/( |

  65. Precalc

    At the point were a line intersects a plane [with the equation (24x+32y+40z=480) and three points of A(5, 10, 1), B(6, 3, 6), and C(12, 1, 4)], the vector i-, vector j-, and vector k-coefficients of the line equal the corresponding values of x, y, and z

  66. Physics

    4. Which of the following is an accurate statement about vectors? A. Rotating a vector about an axis passing through the tip of the vector does not change the vector(definitely not right) B. The magnitude of a vector can be zero even if one of its

  67. physics

    Displacement vectors A,B,and C add up to a total of zero. Vector A has a magnitude of 1550 m and a direction of 24.1° north of east. Vector B has a direction of 41.0° east of south, and vector C has a direction of 33.4° north of west. Find the

  68. physics

    Displacement vectors A, B, and C add up to a total of zero. Vector A has a magnitude of 1550 m and a direction of 22.9° north of east. Vector B has a direction of 41.0° east of south, and vector C has a direction of 35.2° north of west. Find the

  70. Electrostatics

    A linear charge rho L = 2.0 uC lies on the y-z plane. Find the electric flux passing through the plane extending from 0 to 1.0m in the x direction and from -infinity to infinity in the y direction. Alright, so the formula to use is: flux =

  71. Physics

    Let vector A = 4i^ + 4j^, vector B = -2i^ - 5j^, and vector F = vector A - 5(vector B). a) Write vector F in component form. vector F = ? b) What is the magnitude of vector F? F = ? c) What is the direction of vector F? theta = ? Thank you!

  72. Physics

    Let vector A = 4i^ + 4j^, vector B = -2i^ - 5j^, and vector F = vector A - 5(vector B). a) Write vector F in component form. vector F = ? b) What is the magnitude of vector F? F = ? c) What is the direction of vector F? theta = ? Thank you!

  73. Three Dimensions/Calculus

    Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. P= (2,1,2) which is perpendicular to n=i

  75. Calc

    "Let f(x,y)=2(x^2)y-(y^3)+x-4. a) Find the local linearization of f at (3,1) b) Compute the directional derivative of f at (3,1) in the direction towards the point (-2,3). At (3,1), is the function f increasing or decreasing in the direction towards the

  76. mathematics

    A)let AB be the vector with initial point A=(-7,6) and terminal point B=(5,1) 1)Find the component form of AB 2)Write AB--> as a linear combination of the vectors i and j 3)Find the magnitude of AB--> 4)write a unit vector u with the same direction as AB

  77. Pre- Algebra

    Given an equation of a line, how do I find equations for lines parallel to it going through specified points Simplifying the equations into slope-intercept form. 1. y= -2x -4; (1, 3) how do I write the equation of a line parallel to the given line but

  78. Physics

    component of a vector along the two given lines lie in the vertical downward direction making an angle 30 degree with the vertical line are 2 and 4 units.find the magnitude of the original vector and it's direction.

  80. Algebra

    Write a​ slope-intercept equation for a line passing through the point (4,−2) that is parallel to the line 4x+7y=8. Then write a second equation for a line passing through the point (4,−2) that is perpendicular to the line 4x+7y=8. Thank you!

  81. Pre Calculus

    (Graph with line from (-5,0) to (7,2)) Find the direction angle of vector v to the nearest tenth of a degree. Equation editor does not include the grouping symbols "" that are necessary for writing a vector in component form. For this question, use braces

  82. physics

    Vector vector A has a magnitude of 6.90 units and makes an angle of 46.5° with the positive x-axis. Vector vector B also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods find the following. (a) The vector

  83. Math

    For each of the following, find the parametric equations of the line that passes through the point P with direction vector d. In each case, find two points on the line different from P. a) P(1,1) d=(4,-4) b) P(5,0) d=(1,3) answer at the back of the book

  85. Physics

    Vector A with a magnitude of 18 units points in a positive direction. When Vector B is added to Vector A, the resultant Vector points in the negative x direction with a magnitude of 3. What is the magnitude and direction of Vector B? * direction

  86. math

    i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation of the line through the

  87. math

    A vector equation for a given straight line is r = (i + 3j) + lambda (-i - j) Construct a vector equation for the line that does go through the point (1,2), and is perpendicular to r. and Determine the point of intersection of the two lines

  88. math;););)

    Previously you found that a 15-degree counterclockwise rotationcenteredat(2,1)sendsthepoint(4,6)toanother point (x, y) ⇡ (2.638, 6.347). The diagram on the right shows the vector v in the same direction as vector [2,5], only with a di↵erent length.

  90. mathematics vectors

    Relative to the origin O, two points A and B have position vectors a and b respectively. A line, l, passes through A and is parallel to b. It is given that b is a unit vector. (i) Write down a vector equation of l. Show that the position vector of the

  91. mathematics vectors

    Relative to the origin O, two points A and B have position vectors a and b respectively. A line, l, passes through A and is parallel to b. It is given that b is a unit vector. (i) Write down a vector equation of l. Show that the position vector of the

  92. Math

    Find the unit vector that points in the same direction as the vector from the point P=(8,2) to the point Q=(5,9) Find vector PQ, then divide it by its magnitude.

  93. physics

    Displacement vectors A, B, and C add up to a total of zero. Vector A has a magnitude of 1550 m and a direction of 22.9° north of east. Vector B has a direction of 41.0° east of south, and vector C has a direction of 35.2° north of west. Find the

  95. Mathematics

    Write an equation of the line passing through the point (13,-40) and parallel to the line passing the points (1,3) and (7,13). Write your answer in slope-intercept form.

  96. physics

    A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 246 km and a direction 30.0o north of east. The displacement vector B for the second segment has a magnitude of 178 km and a direction

  97. physics

    A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 246 km and a direction 30.0o north of east. The displacement vector B for the second segment has a magnitude of 178 km and a direction

  98. physics

    A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 242 km and a direction 30.0o north of east. The displacement vector for the second segment has a magnitude of 177 km and a direction

  100. Physics

    The acceleration of a particle moving only on a horizontal xy plane is given by , where is in meters per second-squared and t is in seconds. At t = 0, the position vector locates the paticle, which then has the velocity vector . At t = 3.60 s, what are (a)

  101. physics

    Vector vector A has a magnitude of 27 units and points in the positive y-direction. When vector vector B is added to vector A , the resultant vector vector A + vector B points in the negative y-direction with a magnitude of 18 units. Find the magnitude of

  102. maths

    The position vector of the point A(3,4) relative to an origin O is a. (a) Express vector a or (OA) in terms of i and j. (b) Find the magnitude of a. (c) Find the unit vector in the direction of a.

  103. Geometry

    If vector v has an initial point at (2, 3) and a terminal point at (6, 6) and vector w has an initial point at (3, 2) and a terminal point at (6, 6), are the two vectors equivalent? A) Yes, they have the same magnitude and same direction. B) No, they have

  105. Physics/Math

    In the vector sum A + B = C , vector A has a magnitude of 13.1 m and is angled 49° counterclockwise from the +x direction, and vector C has a magnitude of 15.0 m and is angled 20.0° counterclockwise from the -x direction. What are (a) the magnitude and

  106. calculus

    State whether or not the following statements are true. Justify your reasoning.? a. Vector a • (Vector b + Vector c) = Vector a • Vector b + Vector a • Vector c b. Vector a × (Vector b + Vector c) = Vector a × Vector b + Vector a × Vector c c.

  107. College

    If the line passing through point (a,1) and (8,7) is parallel to the line passing through the points (4,9) and (a+2,1) what is the value of a?

  108. Analytic Geometry/Calculus

    We didn't go over the perpendicular form in class, only the parallel. Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line.

  110. Physics

    Given Vector A with magintude 9.17 feet and Vector B with magnitude of 10.58 feet, what is the resultant of the two vectors added together? Answer: I know it would depend on the direction of the vector. If in the same line we would add them or if opposite

  111. Physcis(Please help)

    A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 254 km and a direction 30.0o north of east. The displacement vector for the second segment has a magnitude of 178 km and a direction

  112. Physics or Math

    A force F = 0.8 i + 2.5 j N is applied at the point x = 3.0 m, y = 0 m. Find the torque about the point x = -1.3 m, y = 2.4 m. Hmm, (this is essentially just a vector problem) I know you're supposed to find the position vector r and take the cross product

  113. physics

    Consider three force vectors F1 with magnitude 42N and direction 140°, F2 with magnitude 27N and direction -110°, and F3 with magnitude 19N and direction 120°. All direction angles 0 (0 with a line inside) are measured from the positive x axis:

  115. Physics

    If the expression for a given vector is Vector A-Vector B=(4-5)i^+(3+2)j^ and the magnitude of the difference of the vector is equal to 5.1. What is the direction of the difference Vector A - Vector B. (in the counterclockwise and +x direction)

  116. physics

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

  117. science

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

  118. physics

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

  120. physics

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

  121. physics

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

  122. physics

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

  123. physics

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

  125. science

    The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system for the plane is

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