Angle made by the position vector of the point ( 5 , - 4 , - 3 ) with the positive direction of X - axis is

Step-by-step solution

The position vector of the point 5 ,   - 4 ,   - 3 is 5 i ^ - 4 j ^ - 3 k ^ We know that i ^ is the unit vector along x - axis So, the angle between the vector 5 i ^ - 4 j ^ - 3 k ^ and x - axis will be same as the angle between the vector 5 i ^ - 4 j ^ - 3 k ^ and i ^ . Let the angle be θ ⇒ 5 i ^ - 4 j ^ - 3 k ^ · i ^ = 5 i ^ - 4 j ^ - 3 k ^ i ^ cos θ ⇒ 5 = 5 2 cos θ ⇒ cos θ = 1 2 ⇒ θ = π 4