If a line makes angle `pi/3\ a n d\ pi/4` with x-axis and y-axis respectively, then the angle made by the line with z-axis is `pi//2` b. `pi//3` c. `pi//4` d. `5pi//12`

Explanation

To find the angle made by the line with the z-axis, we can use the relationship between the angles a line makes with the three coordinate axes (x, y, and z). The angles made with the axes are denoted as α (with the x-axis), β (with the y-axis), and γ (with the z-axis).

1. **Given Angles:**
- The angle with the x-axis, α = π/3
- The angle with the y-axis, β = π/4

2. **Using the Relationship:**
The relationship between the angles is given by the equation:
...