How do you find the angle between a vector and the Cartesian coordinate axes If a vector OP = A = A, i+ A j+ A, k makes an angle a with the x -axis, then A x A x cos a = OP A VA, ' + A , + A , If a vector OP = A = A, it A, j+ A, k makes an angle with the y -axis, then Ay Ay A, cos B = OP VA. " + A, + A, If a vector OP = A = A, it A, j+ A, k makes an angle y with the z-axis, then COSY = A z Az A z OP A VA ? + A, " + A, " As for an example OP == 2 i+ 4 j+ 6k makes an angle a , B and y with the x -axis, y-axis and z- axis respectively, then 2 2 2 2 cos a = a = cos (- OP V22 + 42 + 62 V4+16+36 V56' V56 4 4 4 4 cos B = B = cos-1( 4 OP V2 2 + 42 + 62 V4+16+36 V56 ' V56 6 6 6 6 COSY = '4+16+ 36 y = cos-(- 6 42 56 156