The position vectors of three points A, B and C are a, b and c respectively, where c = (cos²θ)a + (sin²θ)b. What is (a × b) + (b × c) + (c × a) equal to?
A.0✓ Correct
B.2c
C.3c
D.Unit vector
Explanation
Since c = (cos²θ)a + (sin²θ)b with cos²θ + sin²θ = 1, the points A, B, C are collinear. For collinear points, (a×b) + (b×c) + (c×a) = 0.
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