math

Find a vector of length 3 that is perpendicular to [2,1,-2]

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  1. First we need a perpendicular, any one will do as long as the dot product is zero. How about

    (2,1,-2)dot(1,4 a) = 0
    2 + 4 - 2a = 0
    -2a = -6
    a = 3

    so (1,4,3) is a normal
    now we have to stretch to a length of 3

    length of my choice = (1/√26)
    so a unit vector is (1/√26)[1,4,3)
    and one of length 3 is

    (3/√26([1,4,3]

    of course this answer is not unique, there would be an infinite number of answers.

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