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If a line is inclined at 60^(@) and 30^(...

If a line is inclined at `60^(@)` and `30^(@)` with the X-and Y-axes respectively, then the angle which makes with the Z-axes is

A

0

B

`(pi)/(4)`

C

`(pi)/(2)`

D

`(pi)/(6)`.

Text Solution

AI Generated Solution

To find the angle that a line makes with the Z-axis when it is inclined at \(60^\circ\) with the X-axis and \(30^\circ\) with the Y-axis, we can use the relationship between the angles and the cosines of those angles. ### Step-by-step Solution: 1. **Understand the relationship**: The angles that a line makes with the X, Y, and Z axes are denoted as \(\theta_1\), \(\theta_2\), and \(\theta_3\) respectively. According to the formula: \[ \cos^2 \theta_1 + \cos^2 \theta_2 + \cos^2 \theta_3 = 1 \] ...
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