If a line makes an angle of `pi/4` with the positive direction of each of x-axis and y-axis, then the angel that the line makes with the positive direction of the z-axis is a. `pi/3` b. `pi/4` c. `pi/2` d. `pi/6`

Options

A. `(pi)/(3)`
B. `(pi)/(4)`
C. `(pi)/(2)`
D. `(pi)/(6)`

Explanation

To solve the problem, we need to determine the angle that a line makes with the positive direction of the z-axis, given that it makes an angle of \( \frac{\pi}{4} \) with both the positive x-axis and y-axis.

### Step-by-Step Solution:

1. **Define Direction Cosines:**
Let the direction cosines of the line be \( L, M, N \), where:
- \( L = \cos(\alpha) \) (angle with the x-axis)
- \( M = \cos(\beta) \) (angle with the y-axis)
...