Question

Let vector a, b and c be three non-coplanar unit vectors such that the angle between every pair of them is π/3. If a x b + b x c = pa + qb + rc where p, q and r are scalars, then the values of (p2 + 2q² + r²)/q²   is _____.

Answer 1

See Fig. 

Given a x b + b x c = pa + qb + rc   (1)

Taking dot product with vector a. Therefore,