85) Let a,→ b→ and c→ be three unit vectors such that a→×b→×c→=32 b→+c→ If b→ is not - Maths -

Question

85) Let a , → b → and c → be three unit vectors
such that a → × b → × c → = 3 2
  b → + c →   I f   b → is not
parallel to c → , then the angle between a →   a n
d   b →   i s   :
(1) 3 π 4
(2) π 2
(3) 2 π 3
(4) 5 π 6

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

We havea→=b→=c→=1a→×b→×c→=32b→+c→⇒b→
a→ c→-c→a→
b→=32b→+32c→Comparing coefficients of c→ on both sides-a→
b→=32⇒a→b→cosα=-32⇒1×1×cosα=cos5π6α=5π6

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85) Let a , → b → and c → be three unit vectors such that a → × b → × c → = 3 2 b → + c → . I f b → is not parallel to c → , then the angle between a → a n d b → i s : (1) 3 π 4 (2) π 2 (3) 2 π 3 (4) 5 π 6