The question wants me to find two vectors orthogonal to <5,3,3> and <1,-1,-3>. I first tried the cross-product only to get the vectors <6,-18,8> and it's opposite <-6,18,-8> but after some research I had to include 1/sqrt(6^2+(-18)^2+8^2) = 1/sqrt(424) and multiply it by the vectors so they would come out as 1/sqrt(424)<6,-18,8> and to it's negative counterpart. Why did I have to include the magnitude of the new vector to get the exact answer?
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See that part I circled in red on the problem? You need to divide by the magnitude of the new vector to get a unit vector.
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