Let a → be a vector which is perpendicular to the vector 3 i ^ + 1 2 j ^ + 2 k ^ . If a → × 2 i ^ + k ^ = 2 i ^ - 13 j ^ - 4 k ^ , then the projection of the vector a → on the vector 2 i ^ + 2 j ^ + k ^ is

Step-by-step solution

Given, a → × 2 i ^ + k ^ = 2 i ^ - 13 j ^ - 4 k ^ Now multiplying both side by 3 i ^ + 1 2 j ^ + 2 k ^ we get, ⇒ a → × 2 i ^ + k ^ × 3 i ^ + 1 2 j ^ + 2 k ^ = 2 i ^ - 13 j ^ - 4 k ^ × 3 i ^ + 1 2 j ^ + 2 k ^ ⇒ 3 i ^ + 1 2 j ^ + 2 k ^ . a → 2 i ^ + k ^ - 6 + 2 a → = i ^ j ^ k ^ 2 - 13 - 4 3 1 2 2 ⇒ 0 - 6 + 2 a → = i ^ j ^ k ^ 2 - 13 - 4 3 1 2 2 a → = 3 i ^ + 2 j ^ - 5 k ^ Now, projection of a → on vector 2 i ^ + 2 j ^ + k ^ is a →