If x → = 3 i ^ - 6 j ^ - k ^ , y → = i ^ + 4 j ^ - 3 k ^ and z → = 3 i ^ - 4 j ^ - 1 2 k ^ , then the magnitude of the projection of x → × y → on z → is

Step-by-step solution

Given x → = 3 i ^ - 6 j ^ - k ^ ,   y → = i ^ + 4 j ^ - 3 k ^ and z → = 3 i ^ - 4 j ^ - 12 k ^ . ⇒ x → × y → = i ^ j ^ k ^ 3 - 6 - 1 1 4 - 3 = i ^ 18 + 4 - j ^ - 9 + 1 + k ^ 12 + 6 = 22 i ^ + 8 j ^ + 18 k ^ = 2 11 i ^ + 4 j ^ + 9 k ^ Now, we know that the projection of a vector a → on b → is defined as a → · b → b → Hence, the magnitude of projection of x → × y → on z → is x → × y → · z &#85