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Find a unit vector r such that r x (-6i + 3j + 2k) = 0 vector (null vector)

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If the vector u = ai+bj+ck, then we have
|i j k|
|a b c| = (2b-3c)i + (-6c-2a)j + (3a+6b)k = 0i+0j+0k
|-6 3 2|
so now solve those three equations for a,b,c

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