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LINES AND PLANES: needs checking

  1. May 21, 2012 #1
    NEED CORRECTION, also this . means dot multiplication.

    My teacher comments:

    #6) you've made some errors (-2 marks)

    #8) correct, they intersect at a point, but you need to find the point like you did in #7 for full marks (-3 marks)


    6.Determine the intersection, if any, of the planes with equations x + y – z + 12 =0 and 2x + 4y - 3z + 8 = 0.

    The normal vectors for the two planes are (1, 1, -1) and (2, 4, -3).
    - These vectors are not collinear therefore the planes intersect in a line.
    x+y-z = -12 (1)
    2x+4y-3z = -8(2)

    -3(1) + 2: -x + y = 28 = x+28
    Let x = t.
    y = t+28
    Substituting in (1)
    One of the either answers=>
    t+t+28-z = -12 or z = 2t+40.
    The parametric equations for the line of intersection are
    x = t, y = 28+t, z = 40+2t.

    8. Give a geometrical interpretation of the intersection of the planes with equations
    x + y − 3 = 0
    y + z + 5 = 0
    x + z + 2 = 0
    N1= (1, 1, 0) N2= (0, 1, 1), N3= (1, 0, 1)
    N1 x N2
    = ((1,1,0) x (0,1,1)) . (1,0,1)
    = (1,-1,1) . (1,0,1)
    =2
    (N1 x N2) . N3 ≠ 0
    Since the triple dot product does not equal to 0, then these three planes must intersect in a single point.
     
  2. jcsd
  3. May 21, 2012 #2

    Mark44

    Staff: Mentor

    For #8 you have a system of 3 equations in 3 variables. You can solve the equations using algebraic techniques, or you can write the equations as an augmented matrix, and then row reduce the matrix.
     
  4. May 21, 2012 #3
    ??? I am confused
     
  5. May 22, 2012 #4

    Mark44

    Staff: Mentor

    Saying that you are confused doesn't help. What are you confused about?
     
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