Ask questions and get helpful responses.
Ask a New Question
  1. Questions

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 point of intersection Q.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Excel

  1. for L1, direction vector is (3,-1,-1)
    and an equation is
    x = 1 + 3t
    y = -t
    z = -1 - t

    for L2, a possible equation is
    x = -6 - 3k
    y = 21 + 9k
    z = -8 - 3k

    if they intersect,
    1+3t = -6-3k AND -t = 21+9k AND -1-t = -8-3k

    using the first two equations,
    1 + 3(-21-9k) = -6-3k
    -62 - 27k = -6-3k
    -24k = 56
    k = 56/-24 = -7/3
    then t = -21 - 9(-7/3) = 0

    does this satisfy the third equation?
    LS = -1-0 = -1
    RS = -8-3(-7/3) = -1
    yes it does!

    so they do intersect and the point of intersection is

    x = 1+3(0) = 1
    y = 0
    z = -1-0 = -1

    they intersect at (1,0,-1)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    Write an equation for a line passing through the points (-1,8 and (0,5)

  2. Math

    1. What is the slope of the line passing through the points (2, 7) and (- 1, 3) ?

  3. Algebra

    Can someone check my answers? 1. Write the equation of the line that passes through point (–2, 3) with a slope of –4. Answer: y = -4x - 5 2. Find the slope and y-intercept. x = –8 Answer: Slope: undefined; y-intercept: none

  4. Math

    how would I find the slope of the line passing through each pair of points in (3, 7) and (6, -11)

  1. 3D Geometry: Intersection of Lines

    Question: Find the equations o the line that intersects the lines 2x + y - 1 = 0 = x - 2y + 3z (say 1) 3x - y + z - 2 + 2 = 0 = 4x + 5y - 2x - 3 (say 2) and is parallel to the line x/1 = y/2 = z/3 (say 3)

  2. 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

  3. Math

    Sara graphs a line passing through points that represent a proportional relationship. Which set of points could be on the line that Sara graphs? A) (2, 4), (0, 2), (3, 9) B) (6, 8), (0, 0), (18, 24) C) (3, 6), (4, 8), (9, 4) D)

  4. math

    find the slope of the line passing through the points (-5,3) and (7,9)

  1. 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

  2. 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.

  3. algebra

    Find the slope of any line perpendicular to the line through the points (0,5) and (-3,-4) Write the equation of the line passing through each of the given pairs of points. Write the answer in slope-intercept form, where possible.

  4. 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,

Still need help? You can ask a new question.