# Does the line [x,y,z]=[5,-9,3]+k[1,-12,2] intersect the plane [x,y,z]=[4,-15,8]+s[1,-3,1]+t[2,3,1]?

20,818 results

### Math

Perry draws two planes, K and L, as shown. Which statement is true? Plane K and plane L contain four lines because a theorem states that a line extends on both sides of a plane. Plane K and plane L intersect along a line because a postulate states that if two planes intersect...

### Geometry

4.Determine which point does not lie on the graph of the line y=x-3 a. (-10, 13) b. (-10-13) c. (-8, -11) A? 8. What is the best model for a tabletop? a. plane b. line c. point d. none of these A? 40. If 2 points lie in a plane, the line containing them ______ a. intersects ...

### Calculus

a) Find parametric equations for the line through (4, 1, 4) that is perpendicular to the plane x − y + 2z = 7. (Use the parameter t.) b) In what points does this line intersect the coordinate planes? xy-plane? yz-plane? xz-plane?

### math( geometry)

indirect proof given: plane M and N intersect; line CD is parallel to plane M; line CD is parallel to plane N; line CD and line AB are not skew prove: line CD is parallel to line AB

### Math

Okay heres the pic. There is a plane with points B,D, and E.those [oints are collinear in the plane. And also outside of the plane is points A, and C. and those points are collinear outside of the plane.thought Line AC intersect at point B of the line BDE.FOr line AC the C is ...

### Geo Hons

Okay heres the pic. There is a plane with points B,D, and E.those [oints are collinear in the plane. And also outside of the plane is points A, and C. and those points are collinear outside of the plane.thought Line AC intersect at point B of the line BDE.FOr line AC the C is ...

### Geometry

Okay heres the pic. There is a plane with points B,D, and E.those [oints are collinear in the plane. And also outside of the plane is points A, and C. and those points are collinear outside of the plane.thought Line AC intersect at point B of the line BDE.FOr line AC the C is ...

### Calc Jacobian

Thanks "I know that the xy region is the line x=y y=0 and y=1- x/2)" It is helpful to rewrite the region in the x-y plane by specifying the three lines and the endpoints, i.e. the points where they intersect. If you insert these points in the formula for U and V you obtain the...

### math

In the xy-plane, lines a and b intersect at point (5,-2), and lines b and c intersect at point (-3,3). What is the slope of line b? Express your answer as a common fraction

### Math- Intesection of a plane and line

Does the line [x,y,z]=[5,-9,3]+k[1,-12,2] intersect the plane [x,y,z]=[4,-15,8]+s[1,-3,1]+t[2,3,1]? If so, how many solutions are there? ( I tried finding the normal vector, there after finding the "d" value to write in scalar equation, and once it is in scalar equation i ...

### geometry

Can lines and planes intersect with each other? Yes. Consider a line perpendicular to your screen on your display you are looking at....the intersection is a point in the plane on the line.

### SAT MATH

In the xy-plane, line m passes through the origin and is perpendicular to the line 8x-3y=n, where n is a constant. If the two lines intersect at the point (r, r-2), what is the value of r?

### Calculus

Where does the line through (1,0,1) and (3,−2,5)intersect the plane x+y+z=10? (x, y, z) =________?

### math

In the xy-plane, line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at the point (t,t+1), what is the value of t? I tried drawing a picture of the problem described above, but I don't understand what I ...

### Geometry

Planes A and B intersect in line s. PLane C intersects A and B, but does not contain s. Draw and label the figure

### trig

which of the following sets gives the x coordinates where the parabola y=x^2+4X-50 and the line y=7x-10 intersect when drawn in the coordinate plane

### trig

which of the following sets gives the x coordinates where the parabola y=x^2+4X-50 and the line y=7x-10 intersect when drawn in the coordinate plane

### Math - Linear Algebra

Let S be the plane defined by x−4y−3z = −18, and let T be the plane defined by −2x+8y+7z = 41. Find the vector equation for the line where S and T intersect. x 0 0 y = 0 + t0 z 0 0

### Calc

Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 427 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is ...

### Calc

Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 427 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is ...

### 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.

### Geometry

I need help with these problems: 11. The 2 captains of the school football team meet with the 3 captains of another team for the coin toss. If each captain shakes hands with each captain from the opposing team, how many different handshakes occur? 14. Find the maximum area of ...

### calculus

Two commercial airplanes are flying at an altitude of 40,000 ft along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 429 knots (nautical miles per hour; a nautical mile is 2000 yd or 6000 ft.) Plane B is ...

### math (please help steve)

Circles Γ1 and Γ2 have centers X and Y respectively. They intersect at points A and B, such that angle XAY is obtuse. The line AX intersects Γ2 again at P, and the line AY intersects Γ1 again at Q. Lines PQ and XY intersect at G, such that Q lies on line ...

### Math (please help steve)

Circles Γ1 and Γ2 have centers X and Y respectively. They intersect at points A and B, such that angle XAY is obtuse. The line AX intersects Γ2 again at P, and the line AY intersects Γ1 again at Q. Lines PQ and XY intersect at G, such that Q lies on line ...

### Math; Solve by Graphing

Which description best describes the solution to the following system of equations? y = −x + 4 y = 3x + 3 Line y = −x + 4 intersects the line y = 3x + 3. Lines y = −x + 4 and y = 3x + 3 intersect the x-axis. Lines y = −x + 4 and y = 3x + 3 intersect the...

### Math

1. Name the intersection of plane ACG and plane BCG. A. AC B. BG C. CG D. The planes need not intersect. Is the answer C? this is hard for me since there isn't a picture. Thank you!

### Math - distance b etween a line and plane

Find the distance between the parallel line and the plane. line: vector r = [2,0,1]+t[1,4,1] plane: 2x-y+2z=4

### Math- intersection of planes

Show that the line [x,y,z]=[10,5,16]+t[3,1,5] is contained in the plane x+2y-z-4=0 I tries writing the vector equation in parametric form and then substituting it into the respective x,y,z in the plane, after simplifying I get 0t=0 does this mean that the line is in the plane ...

### Vectors

Show that the line with parametric equations x = 6 + 8t, y = −5 + t, z = 2 + 3t does not intersect the plane with equation 2x − y − 5z − 2 = 0.

### 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 intersection Q. ...

### Math

1. Plane hkp and plane rkp are two distinct planes. name the intersection of the plane hkp and plane rkp. A) Ray KP B) Ray HK C) Ray RP D) The planes need not intersect. Is the answer A? Please correct me if I am wrong. Thank you!

### Calculus II

Here's the problem: Find the area of a plane region bounded by y=x^3 and its tangent line through (1,1). So far I have the graph on my graphing calc, so I have an idea at what I'm looking at. I found the tangent line to y=x^3 to be y=3x-2. Now I am stuck. I am trying to find ...

### Calculus

determine the equation of a plane, P3, that intersects the planes P1: x + y + 3z − 2 = 0 and P2: x − y + 2z = 0 in a point; a line. I know the normals are (1,1,3) and (1,-1,2) clearly the lines don't intersect because the normals are't multiples. So I don't know ...

### Geometry

I don't get these questions Is there exactly one plane containing two non intersecting lines? and if a line is perpendicular to a plane, is it perpendicular to every line in the plane?

### Math

In the diagram below of triangle TEM, medians line TB, line EC and line MA intersect at A, and TB = 9. Find the length of TD.

### geometry

in the diagram below of triangle TEM, medians line TB, line EC and line MA intersect at D, and TB = 9. Find the length of TD.

### geometry

in the diagram below of triangle TEM, medians line TB, line EC and line MA intersect at D, and TB = 9. Find the length of TD.

### Calculus

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. If the planes intersect in a line, determine a...

### maths

Let ABC be a triangle.Draw median AD on BC.Draw median AE of triangle ABD on BD.Take a point on side AB say F and join CF. Now from D make a line parallel to CF such that the line cuts AB at G. Note- G lies between F and B. AD intersect CF and P. AE intersect GD at H. So BD=DC...

### Physics

A supersonic jet travels at 3.0 Mach (i.e. at three times the speed of sound). It cruises at 20,000 m above the ground. we choose t=0 when the plane passes directly overhead of an observer. At what time t will the observer hear the plane? -- there is a diagram of a person ...

### math

the axes are rectangular and a point P moves on the fixed plane lx+my+nz=p.the plane through P perpendicular to OP meets the axes in A,B,C parallel to YOZ,ZOX,XOY intersect in Q.show that the locus of Q is p{1/x2+1/y2+1/z2}=l/x+m/y+n/z

### finite math

Given n(A')=23, n(B')=16, and n((A [intersect] B) U (AUB)'))= 24, find (A [intersect] B) I apologize but intersect was the best way I found to represent the upside down U symbol.

### Linear Algebra

Last number from the sample test! A plane P passes by the coordinates: A(1,0,-7); B(-2,-1,0); C(0,0,-3) Using the equation of the line D: x= 7+12t, y= -1-6t, z= 2-2t, Find the equation of a line that's entirely part of the plane P and that is perpendicular to the line D at ...

### analytical geometry

the axes are rectangular and a point P moves on the fixed plane lx+my+nz=p.the plane through P perpendicular to OP meets the axes in A,B,C parallel to YOZ,ZOX,XOY intersect in Q.show that the locus of Q is p{1/x2+1/y2+1/z2}=l/x+m/y+n/z

### Maths - Linear Relations Simple Problem

Find the values of m for which the line with equation y=mx+2 does not intersect the parabola with equation y=(x-1)^2 + 5. I am not sure how to solve this problem. I know that both equations equal each other when it intersects but what happens if they don't intersect. Please ...

### Calc.

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. If the planes intersect in a line, determine a...

### Calc.

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. If the planes intersect in a line, determine a...

### math

Given the plane 2x-3y+7z=4, a) Find the equation for the line perpendicular to the plane that intersects the plane at the point P=(6,5,1). b) How far is it from the point (4,-2,3) to the plane?

### Calculus

Consider the line through the points (3,2,5) and (1,1,1). Consider the plane A that is perpendicular to this line, and passing through the point (-1,0,2). Consider the plane B that passes through the points (1,-1,0), (0,2,0), and (0,5,2). Consider the intersection of plane A ...

### math

19. Which statement describes the relationship between the line graphs of the equations below? y=-2x+4 y=0.5x+4 A.The line graph are the same line. B.The line graph are parallel lines. C.The line graph are perpendicular lines. D.The line graphs intersect, but are not ...

### Math! Please check!

Name the intersection of planes ADE and BEA. A- plane BED B- plane ABC C- line BD D- line AE My choice is D. (Sorry that I could not post an image)

### math

georgia is constructing a line perpendicular to xz at point x.with x as a center,she drew two arcs that intersect xz at points w and y.what is the next step she should take? a.set the compass wider and use points w and y as centers to draw arcs that intersect above xz. b....

### Physics

Let vector B = 8.8 m, 75 degrees counterclockwise from the vertical. a) Find the x- and y-components of vector B in the normal coordinate system (where x is a horizontal line and y is a vertical line...both intersect each other). b) Find the x- and y-components of vector B in ...

### Math

Given the plane 2x-3y+7z=4, find the equation for the line perpendicular to the plane that intersects the plane at the point (6,5,1).

### Pre-calc

The plane y + 4z = 15 intersect which axes?

### Trigonometry - Cosine of angle

What is the cosine of the angle between two adjacent faces of a regular tetrahedron? (We define the angle between two intersecting planes as the angle between two intersecting lines, one in each plane, such that each line is perpendicular to the line at which the planes ...

### algebra

write equation of line that passes through P(0,0) and is parallel to given line, x=8y-16, answer in slope intersect form.

### geometry

Alex plots 4 points K, L, M, and N. He joins points K and L and points M and N with straight lines as shown. Alex made the following statements about the points. Statement 1: and intersect on the same plane. Statement 2: and intersect at point P. Which chart best justifies ...

### Precalculus

I know I posted this question already ,but I posted the wrong one.... Sets A,B and C are subsets of U. U= positive integers less than 16 A= prime numbers B= factors of 36 C= multiples of 4 (A intersect B)' INTERSECT C {?} I meant INTERSECT not union! My answer: 4,8,12

### math

L is a straight line in x-y plane. its equation is in the form y-8=m(x-1) determine all points in x-y plane where line L intersects curve y=2x^2 i know that 1,8 is a point on the line. I'm not sure what points the question is looking for here. Without knowing what m is, every ...

### precalc

I;m not sure if i am doing this right...I keep getting a negative intersection point, which doesn't seem possible. Please help! a) find the equatoin of line 1 which passes through (1,3) and (9,7) I get y=3+1/2(x+1)or y=1/2x+2.5 b) the line 2 is perpedicular to line 1 and ...

### maths --plse help me..

how to find the cartesian eqn of plane passing through A(0,0,0) and B(3,-1,2) and parellel to line (x-4)/1 = (y+3)/-4 = (z+1)/7 basically how to find a plane parallel to a given line??

### Algebra

The solutions to the equation f(x)=g(x) are -2 and 1.If f(x) and g(x)graphed on the same coordinate plane, where do they intersect

### ALGEBRA 1

solve by graphing 3x+2y=8 6x+4y=16 You need to graph the 2 equations, and find where they intersect. That is your solution. Somebody is pulling your leg: These are the same lines, there is no solution. I UNDERSTAND i NEED TO FIND WHERE THEY INTERSECT. THE QUESTION IS do how do...

### Math

If line A is a perpendicular bisector of MN, then which of the following statements is NOT true? 1)line A and MN intersect at a right angle 2)line A splits MN into two congruent segments 3)MN splits line A into two congruent segments 4)line A intersects MN at the midpoint of ...

### Math 10

1 more question.... how would I make this equation perpendicular? The question is.... The line Y=3x-1 and a line perpendicular to it intersect at R(1,2). Determine the equation of the perpendicular line. Can someone please tell me the steps to making that line perpendicular? ...

### algebra

In a coordinate plane, the points (2,4) and (3,-1) are on a line. Which of the following must be true? 1. The line crosses the x-axis. 2. The line passes through (0, 0). 3. The line stays above the x-axis at all times. 4. The line rises from the lower left to the upper right. ...

### Integrated Math 1

The parabolas y = -3x2 + 10x - 6 and y = -3x2 - 17x + 2 intersect at _____? A.the line y = 27x - 8. B. x=the square root of 2 over 3 and xthe -square root of 2 over 3. C. x=8/27. D. they do not intersect.

### Pre Calc

A plane (A) heading south at 120 mph and a plane (B) heading west at 600 mph are rlying tword the same point at the same altitude. Plane A is 100 miles from the point where the flight patterns intersect and plane B is 550 miles from there. A) Find the parametric equation that ...

### Math

Line m is perpendicular to plane A. how many planes can contain line m and alo be perpendicular to plane A? I think it my be infinite?

### Calculus

At what point does the normal to y=-5-1x+3x^2 at (1, -3 ) intersect the parabola a second time? Answer: Note: You should enter a cartesian coordinate. The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are negative reciprocals -- ...

### 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 for the plane. By ...

### Calculus

Verify please and thank you~ Does the line (x-7)/3=(y+8)/6=(z+4)/5 and the point P(10,-2,1) determine a plane? Answer: Yes, it is a plane because when I substituted the point P(10,-2,1) into the equation, I got the coordinates (1,1,1) If the coordinate became to be (0,0,0) ...

### Geometry

a line RS is perpendicular to plane p at R. If T is a second point not on. Can RT be perpendicular to plane P? Lines AB and LM are each perpendicular to plane P. Are AB and LM coplanar? Plan P is perpendicular to AB at B. Plane Q intersects AB at P. Can Q be perpendicular to AB?

### Math

a line RS is perpendicular to plane p at R. If T is a second point not on. Can RT be perpendicular to plane P? Lines AB and LM are each perpendicular to plane P. Are AB and LM coplanar? Plan P is perpendicular to AB at B. Plane Q intersects AB at P. Can Q be perpendicular to AB?

### Calculus and vectors

Verify please and thank you~ 1. Does the line (x-7)/3=(y+8)/6=(z+4)/5 and the point P(10,-2,1) determine a plane? Answer: Yes, it is a plane because when I substituted the point P(10,-2,1) into the equation, I got the coordinates (1,1,1) If the coordinate became to be (0,0,0) ...

### maths

A(–4, 3), B(3, 7), C(0, –1) and D(–7, –5) are the vertices of a parallelogram on the Cartesian plane. Determine the coordinates of the point where the diagonals of ABCD intersect.

### MATH

Region A that on xy-plane is bounded by two (2) curves and a line. The curves are y=x^3-2x+3 and y=-x^2+3 while the line is x=0. It is located in the first quadrant of xy-plane. Determine the area of region A.

### Geometry

Hi, I have to use algebra to find the coordinates of the point where two lines intersect, the first line passes through the points 4,3 and 10,0 and the second line is y=6. Any ideas would be very much appreciated, many thanks

### Math

Solve the system by graphing. x+y=−2 y=13x+2 A. (6, 4); The image is of a 2-dimensional graph with an x-axis and a y-axis. One line is drawn passing through co-ordinates (-3,1) and (3,3). Another line is drawn from co-ordinate (-2,-4) to (6,4). B. (−3, 1); The ...

### physics

An electrically neutral model airplane is flying in a horizontal circle on a 2.0-m guideline, which is nearly parallel to the ground. The line breaks when the kinetic energy of the plane is 50 J. Reconsider the same situation, except that now there is a point charge of +q on ...

### Math calculus 2

Let S be the region of the xy-plane bounded above by the curve ((x^3)*y)=64, below by the line y=1, on the left by the line x=2, and on the right by the line x=4. Find the volume of the solid obtained by rotating S around (a) the x axis (b) the y axis (c) the line x=2

### geometry

Choose the phrase that completes the following statement as stated by the point, line, and plane postulates: Once plane___________ passes through three noncollinear points. a. never b. sometimes c. always d. point, line, and plane postulates do not address this topic directly.

### Geometry- trig ratio

An observer (o) spots a plane flying at a 55 degrees angle to his horizontal line of sight. if the plane is flying at an altitude of 21,000 ft, what is the distance (x) from the plane (p) to the observer (o)?

### physics

a plane is flying with a constant speed along a straight line at an angle 60degree with the horizontal. the weight(W) of the plane is 90,000N and its engine provides a thrust(T)of 120,000N in the direction of flight . two additional forces are exerted on the plane :the lift ...

### Trigonometry

An observer (0) spots a plane flying at a 55 degree angle to his horizontal line of sight.If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (0)

### Math

At what points does the line y+x-3=0 intersect the curve 2y=6x+2(x^2)-(y^2)?

### Vectors

At what point does the line r=(-2,3,1)+s(2,3,-1) intersect the y-axis?

### geometry

An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?

### maths - geometry

In a space with an orthonormal coordinate system consider the plane; &: 4x-3y=12 (a)(i)Find the coordinates of the points of intersection of the plane & with the coordinates axes (=axes intersections???) (ii)Find the parametric equations for the line of intersection of the ...

### math

Hi I wanted to check my work for this problem. Consider the points A(1,0,0) B(2,2,2) and C(0,2,1). 1) Find the vector CA x CB I got -2i -3j +4k for this 2) Find an exact value for the area of the triangle ABC. I got sqrt29/2 for this. 3) Plane II(1) is 2x+3y-4z=2. A second ...

### calculus

Find parametric equations for the line that is perpendicular to the plane 2x-y+3z=7 and intersects the plane when x=1 and y=1.

### calculus

Find an equation of the plane containing the line of intersection of x+y+z=1 and x−y+2z=2, and perpendicular to the x-y plane.

### math

for what values of k in y=3x+k with the curve y=-x^2-3x+6 intersect the line at 2 points

### Math (urgent)

the equation x^2+y^=25 describes a circle with center at the origin and radius 5. The line y=x-1 passes through the circle. Using the substitution method, find the points at which the circle and line intersect. a) (4,3) and (-4,-3) b) (3,4) and (-3,-4) c) (4,-3) and (-3,4) d) ...

### Calculus

Find the scalar equation of a plane that is perpendicular to plane r=(-2,1,3)+s(0,1,1)+t(-1,0,3) and also intersects it along the line (x-3)/2=(y+1)/-3,z=1

### math

Hi, I was working on my math homework and I was stumbling on these problems. I tried looking at the solutions but my answers were completely off. Here are the ones I'm stuck on: If vectors O(0,0,0), A(6,0,0), B(6,-sqrt(24), sqrt(12)), and C(0,-sqrt(24), sqrt(12)) form a square...

### Geometry

plane hkp and plane rkp are 2 distinct planes. Name the intersection of plane hkp and rkp my answer is line kp