If a line makes angles ⁻¹ 7 , ⁻¹ 5 3 with X -axis, Y -axis respectively, then the angle made by it with Z -axis is

Step-by-step solution

A line makes angle ⁻¹ 7 and ⁻¹ 5 3 with X -axis and Y -axis respectively. So, Sc aligned & = ⁻¹ 7 & = 7 & = 1 8 & and & = ⁻¹ 5 3 & = 5 3 & = 3 8 & aligned Let angle make with Z -axis is . So, aligned & ^2 + ^2 + ^2 =1 & ( 1 8 )^2+ ( 3 8 )+ ^2 =1 & 4 8 + ^2 =1 1 2 + ^2 =1 aligned array lr & ^2 = 1 2 & = 1 2 & = 1 2 or -1 2 & = 4 or - 4 & = 4 or 3 4 array So, angle made by line with Z -axis is 4 and 3 4 .