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Let vec(a), vec(b), vec(c) be three non-...

Let `vec(a), vec(b), vec(c)` be three non-zero vectors such that `vec(c)` is a unit vector perpendicular to both `vec(a)` and `vec(b)`. If the angle between `vec(a)` and `vec(b)` is `pi//6`, then prove that `[vec(a)vec(b)vec(c)]^(2) = (1)/(4)|vec(a)|^(2)|vec(b)|^(2)`.

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The correct Answer is:
`(1)/(4)|vec(a)|^(2)|vec(b)|^(2)`
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