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Question

The two vectors [111] and [1aa2] where a= 12+j32 and j = 1 are

A
orthonormal
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B
orthogonal
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C
parallel
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D
collinear
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Solution

The correct option is B orthogonal
Let X1=111 and X2=1aa2=1ww2
a=12+i32=w (Cube root of unity)

Now X1.X2=1×1+1×w+1×w2
=1+w+w2=0

Hence they are orthogonal.

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