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Math Help - Two vector questions (high school level)

  1. #1
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    Two vector questions (high school level)

    1) Expand and simplify: (-2a + 3b) dot (5a - b). (a and b being vectors)

    2) Explain how to prove if 4 given points are coplanar. Determine if A(3, 1, 0), B(2, -3, 1), C(-1, 0, 4) and D(5, -6, -2) are coplanar.

    Thanks, I'm completely stumped on both.
    Last edited by TheJacksonater; July 27th 2008 at 05:36 PM.
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  2. #2
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    Hi,
    a.)

    (-2a+3b).(5a-b)
    =(-2)(5)+(3)(-1)
    =-10-3
    =-13

    b.)

    Give point A(3,1,0); B(2,-3,1): C(-1,0,4); D(5,-6,-2)

    A=3i+j; B=2i-3j+k; C=-i+4k; D=5i-6j-2k

    5i-6j-2k=x(3i+j)+y(2i-3j+k)+z(-i+4k)
    5i-6j-2k=(3x+2y-z)i+(x-3y)j+(y+4z)k
    here equation the like vectors
    3x+2y-z=5
    x-3y=-6
    y+4z=-2

    solve x , y and z values
    and substitute in one of the equation
    if its satisfies then the given vectors are coplanar

    all the best
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  3. #3
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    I got a question too
    for second question can we just do

    AB, BC, CD

    and then use the triple scalar product
    AB . (BC X CD)

    if that equals zero then it means they are coplanar

    will that work?

    Thanks in advance







    -----------------------------------
    AB = [-1, -4, 1]
    BC = [-3, 3, 3]
    CD = [6, -6, -6]


    AB . (BC X CD)

    [-1, -4, 1] . [0, 0, 0]

    = 0

    which means they are co planar

    can anyone plz verify this one from me (whether this method is correct or not)
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