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11 June, 12:24

Find b and c so that (7, b,

c. is orthogonal to both (1, 2, 3) and (1, - 2, 1).

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Answers (1)
  1. 11 June, 13:03
    0
    The cross product is perfect for this purpose.

    The cross product C of vectors p and q is orthogonal to both p and q.

    C will then be scaled to have the first value equal to 7 to find b and c.

    C=x

    =

    i j k

    1 2 3

    1 - 2 1

    =

    =

    =2

    = (8/7)

    = (8/7)

    So b=7/4, c=-7/5

    Check:

    . = 7*1+7/4*2-7/5*3=7+7/2-21/2=0 ... ok, orthogonal

    .=7*1-7/4*2-7/2*1=0 ... ok, orthogonal
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