Vectors

Consider the 2 lines with equations (x+8)/1=(y+4)/3= (z-2)/1 and (x,y,z)=(3,3,3)+t (4,-1,-1), tER.

Find the point of intersection of the lines.

So I that these 2 lines are perpendicular because if you do the dot product of their direction vectors you get zero.

L1:
x=-8+s
y=-4+3s
z=2+s

L2:
x=3+4t
y=3-t
z=3-t

So I tried setting L1=L2 for each variable,x,y and z.

Then doing elimination yo solve for s and t and sub them back into my original parametric equations but I don't get the answer.

What do I need to do?

The answer key says the answer is (-5,5,5)

  1. 👍 0
  2. 👎 0
  3. 👁 110
  1. I set the x and y equations equal to each other to get:
    4t - s = -11
    t + 3s = 7
    solving these, I got t = -2 and s = 3
    which verified in the z value of 0 for both lines.
    So sub s=3 and t = -2 and it the corresponding lines and you get
    (x,y,z) = (-5,5,5)

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Explain fully please and thank you! =) Determine the point of intersection of the lines L1: r= (1,3,7) + s(1,2,-2),seR and L2: v=(0,2,-3) +t(1,1,4), teR. a) P(1,3,1) b P(1,3,7) c) The lines coincide d) no point of intersection

    asked by Melissa on April 7, 2012
  2. Math

    1. Two lines, C and D, are represented by the following equations: Line C: y = x + 5 Line D: y = −2x − 1 Which of the following options shows the solution to the system of equations and explains why? (−2, 3), because the

    asked by Bobby Adams on April 6, 2017
  3. algebra

    Two lines, C and D, are represented by the following equations: Line C: y = x + 5 Line D: y = −2x − 1 Which of the following options shows the solution to the system of equations and explains why? (−2, 3), because the point

    asked by anan on October 7, 2015
  4. Vectors

    I am really lost and confused! Consider the lines r = (1,-1,1) + t(3,2,1) and r = (-2,-3,0) + u(1,2,3). a) Find their point of intersection. b) Find a vector equation for the line perpendicular to both of the given lines that

    asked by Alex on April 7, 2008
  5. MATH PLS HELP CHECK ANSWERS

    3. What is the rule for the function shown in the table? (1 point) x = -1, 0, 1, 2 y = -2, 1, 4, 7 A.y = 1/3x + 1 B.y = 3x + 1 C.y = 1/3x D.y = 1/2x + 1 4. What is the function rule for the following situation? rex paid $20 for a

    asked by TTR+S<3 on May 8, 2014
  6. precals

    find the equations of the lines to the line whose equations is y-17 / x -13 = -3 /2 If these lines each pass through the point (6,-5) Gracias`

    asked by treeema on April 25, 2010
  7. math

    What will the graph look like for a system of equations that has no solutions? A. The lines will be perpendicular. B. The lines cross at one point. C. Both equations will form the same line. D. The lines will be parallel. Is the

    asked by Claire on April 30, 2015
  8. Algebra

    6. y = 2x - 1 and y = x + 3 ***A. (4,7) B. (7, 4) C. (-7, -4) D. infinite solutions 7. y = 4x and y + x = 5 A. (-4, 1) B. (1, 4) C. (-3, 2) ***D. (2,3) 8. What will the graph look like for a system of equations that has no

    asked by Leet Speaker on March 1, 2016
  9. Math

    What will the graph look like for a system of equations that has no solution? A. The lines will be perpendicular. B. The lines will cross at one point. C. Both equations will form the same line. D. The lines will be parallel. I

    asked by Cassie on April 9, 2013
  10. cal

    Equations of the tangent lines to hyperbola xy=1 that pass through point (-1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (-1,-1)? You're correct, the graph

    asked by Melba on September 26, 2006

More Similar Questions