A line makes `30^(@), 120^(@)` and `90^(@)` angles from the positive direction of x-axis, y-axis and `pi`-axis respectively. Find its direction cosines.

Explanation

To find the direction cosines of a line that makes angles of \(30^\circ\), \(120^\circ\), and \(90^\circ\) with the positive directions of the x-axis, y-axis, and z-axis respectively, we can follow these steps:

### Step 1: Understand the definition of direction cosines
Direction cosines are the cosines of the angles that a line makes with the coordinate axes. If a line makes angles \(\alpha\), \(\beta\), and \(\gamma\) with the x-axis, y-axis, and z-axis respectively, the direction cosines \(l\), \(m\), and \(n\) are given by:
\[ l = \cos \alpha, \quad m = \cos \beta, \quad n = \cos \gamma \]

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