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Vector Algebra

Question

Let, a, b and c be three non-zero vectors such that no two of them are collinear and $left parenthesis straight a space xb right parenthesis space straight x space straight c space equals space 1 third vertical line straight b vertical line vertical line straight c vertical line straight a.$ if θ is the angle between vectors b and c, then a value of sin θ is

$fraction numerator 2 square root of 2 over denominator 3 end fraction$
$fraction numerator negative square root of 2 over denominator 3 end fraction$
$2 over 3$
$fraction numerator negative 2 square root of 3 over denominator 3 end fraction$

Solution

fraction numerator 2 square root of 2 over denominator 3 end fraction