Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are `1/(sqrt(3)),1/(sqrt(3)),1/(sqrt(3))`.

Explanation

To show that the direction cosines of a vector equally inclined to the axes OX, OY, and OZ are \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \), we can follow these steps:

### Step 1: Define the angles of inclination
Let the angles of inclination of the vector with the x-axis, y-axis, and z-axis be denoted as \( \alpha \), \( \beta \), and \( \gamma \) respectively. Since the vector is equally inclined to all three axes, we have:
\[ \alpha = \beta = \gamma \]

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