Let a → = a i i ^ + a 2 j ^ + a 3 k ^ and b → = b 1 i ^ + b 2 j ^ + b 3 k ^ be two vectors such that | a → | = 1 ; a → · b → = 2 and | b → | = 4 . If c → = 2 ( a → × b → ) - 3 b → , then the angle between b → and c → is equal to :

Step-by-step solution

Given | a → | = 1 , | b → | = 4 , a → · b → = 2 Also, c → = 2 ( a → × b → ) - 3 b → . . . i Applying dot product with a → on both sides of equation i ⇒ c → · a → = - 6 . . . i i as ( a → × b → ) · a → = ( a → × b → ) · b → = 0 Again, applying dot product with b → on both sides of equation i ⇒ b → · c → = - 48 . . . i i i Now, using equation i ⇒ c → 2 = 4 | a → × b → | 2 + 9 | b → | 2 - 12 a → × b → · b → We know that, a → × b → 2 + a → . b → 2 = a → 2 b → 2 ⇒ | c → | 2 = 4 | a → | 2 | b → | 2 - ( a → · b → ) 2 + 9