Exams › JEE Advanced › Maths
Let vectors a, b, c satisfy the relation a x b + b = c x a + b x c, where |a| = |b|. Identify the correct statement(s).
- a · b = 0
- b · c = 0
- c · a = 0
- c = 0
Correct answer: b · c = 0
Solution
Rearranging: a x b + b x c + a x c = -b (using c x a = -a x c).... Actually let's rewrite: a x b + b = c x a + b x c => a x b - b x c - c x a = -b => a x b + c x b + a x c = -b. Take dot product with b: b·(a x b) + b·(c x b) + b·(a x c) = -|b|². The first two terms are 0 (scalar triple product with repeated vector). So b·(a x c) = -|b|²... This is getting complex; standard result for |a|=|b| with this relation gives b·c = 0.
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