Let a, b, c be unit vectors. Further, a is perpendicular to b; c makes an angle π/3 with both a and b; and c = pa + qb + r(a×b). What is the value of (p+q)?

Given a·b = 0, |a| = |b| = |c| = 1, and c·a = cos(π/3) = 1/2, c·b = 1/2. Taking dot product of c = pa + qb + r(a×b) with a: c·a = p|a|² + q(a·b) + r·a·(a×b) = p + 0 + 0 = p. So p = 1/2. Similarly c·b = q = 1/2. Therefore p + q = 1/2 + 1/2 = 1.