Let a → ,   b →     and    c → be three non - zero vectors such…

Let a→, b→  and  c→ be three non - zero vectors such that no two of them are collinear and a→×b→×c→=13b→c→a→. If θ is the angle between vectors b→ and c→, then a value of sinθ is 

  1. - 2 3 3
  2. 2 2 3
  3. - 2 3
  4. 2 3

Solution

Given a→ × b→ × c→= 13 b→ c→a→

a→⋅c→ b→- b→⋅c→ a→=13 b→c→ a→

⇒ a→⋅c→=0  and  b→⋅c→= -13 b→c→

b→c→cosθ= -13 b→c→

cosθ= -13

sinθ= 1-19= 89 = 223

Asked in: JEE Main 2015 (04 Apr)

Practice more Vector Algebra questions on Aicharya