A vector ` vec r` is inclined at equal acute angles of `x-axis ,` `y-axi s` and `z-a xi sdot` if `| vec r|=6` units, find ` vec rdot`

Explanation

To solve the problem, we need to find the vector \(\vec{r}\) that is inclined at equal acute angles to the x-axis, y-axis, and z-axis, given that \(|\vec{r}| = 6\) units.

### Step-by-Step Solution:

1. **Understanding the Angles**:
Since the vector \(\vec{r}\) is inclined at equal angles to the x-axis, y-axis, and z-axis, we can denote these angles as \(\alpha\), \(\beta\), and \(\gamma\). Given that they are equal, we can write:
\[
\alpha = \beta = \gamma
...