Let a → = x i ^ + y j ^ + z k ^ and x = 2 y . If a → = 5 2 and a → makes an angle of 135 ° with the z -axis then a → =

Step-by-step solution

Given a → = x i ^ + y j ^ + z k ^ a → = x 2 + y 2 + z 2 = 5 y 2 + z 2   ∵ x = 2 y i.e. 5 y 2 + z 2 = 5 2 ⇒ 5 y 2 + z 2 = 50 a → · k ^ = a → cos 135 ° ⇒ z = 5 2 × - 1 2 = - 5 Now, 5 y 2 = 25 ⇒ y = ± 5 ,   x = ± 2 5 i.e. a → = ± 2 5 i ^ ± 5 j ^ - 5 k ^