Let a→, b→ and c→ be non-zero vectors such that a→×b→×c→=13 b→ c→ a→ If θ is the acute - Maths - Vector Algebra

Question

Let a → ,   b →   and   c → be
non-zero vectors such that a → × b → × c
→ = 1 3   b →   c →   a → If
θ is the acute angle between the vectors b →   and
  c → , then sin θ equals-
(A) 1 3 (B) 2 3 (C) 2 3 (D) 2 2 3

Lovina Kansal · Accepted Answer

Dear student
We have,a×b×c=13bca⇒2a cb-b ca=13bca⇒a
cb=13bc+b ca⇒a c=0 and 13bc+b
c=0⇒bc13+cosθ=0⇒13+cosθ=0⇒cosθ=-13⇒sinθ=223     using pythagoras theorem
Regards

Let a → , b → and c → be non-zero vectors such that a → × b → × c → = 1 3 b → c → a → . If θ is the acute angle between the vectors b → and c → , then sin θ equals- (A) 1 3 (B) 2 3 (C) 2 3 (D) 2 2 3