If P → = 3 i ^ + 3 j ^ + 2 k ^ and Q → = 4 i ^ + 3 j ^ + 2 . 5 k ^ then, the unit vector in the direction of P → × Q → is 1 x ( 3 i ^ + j ^ - 2 3 k ^ ) . The value of x is

Step-by-step solution

Unit vector in the direction of P → × Q →   is   n ^ = P → × Q → | P → × Q → | . Here, P → × Q → = i ^ j ^ k ^ 3 3 2 4 3 2 . 5 = 3 i ^ 2 + j ^ 2 - 3 k ^ And P → × Q → = 3 2 2 + 1 2 2 + 3 2 = 4 = 2 ⇒ P → × Q → | P → × Q → | = 1 2 3 i ^ 2 + j ^ 2 - 3 k ^ = 1 4 ( 3 i ^ + j ^ - 2 3 k ^ )    ⇒ x = 4