Math: Vectors

Find any vector w that is perpendicular to both vector "u = 3j + 4k" and vector "v = 2i".

Note: i, j and k are unit vectors

How would you solve this problem? Please walk me through?

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  1. Two vectors are perpendicular if their dot product is zero
    so you want a vector w = (a,b,c) so that
    (a,b,c)∙(0,3,4) = 0 and
    (a,b,c)∙(2,0,0) = 0

    from the second 2a = 0, so a=0
    from the first 3b+4c=0
    or 3b=-4c
    b/c = -4/3, if we let c=3 and b=-4 that would work
    Notice there is more than one solution
    as long as our vector w has direction (0,-4,3)

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