Ask questions and get helpful answers.

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 intersection Q.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩

1 answer

  1. L1:
    r1= (2,-2,5) + s<6,4,2>
    x = 2 + 6s
    y = -2 + 4s
    z = 5 + 2s

    L2:
    r2 = (7,4,0) + t<-1,-2,3>
    x = 7 - t
    y = 4 - 2t
    z = 0 + 3t

    If they intersect, then their corresponding x, y , and z values must be the
    same for some constant s and t

    I will set the y's and z's equal,
    -2 + 4s = 4 - 2t ---> 4s + 2t = 6 ----> 2s + t = 3
    5 + 2s = 3t
    2s - 3t = -5

    subtract those last two:
    4t = 8
    t = 2

    sub into 2s+t=3
    2s + 2 = 3
    s = 1/2

    then in L1, z = 5 + 2s = 5+5/2 = 15/2
    in L2, z = 3t = 6

    I did not get the same value, so the two lines do not intersect

    better check my calculations, only had one coffee so far.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Related Questions

Still need help?

You can ask a new question or browse existing questions.