Let a, b, c be unit vectors. Further, a is perpendicular to b; c makes an angle of π/3 with both a and b; and c = pa + qb + r(a × b). What is the value of (p + q)?
A.1/2
B.1✓ Correct
C.3/2
D.2
Explanation
Taking dot product with a: c·a = p(a·a) + q(a·b) + r(a×b)·a = p(1) + q(0) + 0 = p. Given c·a = |c||a|cos(π/3) = 1/2. So p = 1/2. Similarly, taking dot product with b: c·b = q = 1/2. Therefore p + q = 1/2 + 1/2 = 1.
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