If a unit vector ` vec a` makes an angle `pi/3` with ` hat i ,\ pi/4` with ` hat j` and an acute angle `theta` with ` hat k` then find `theta` and hence, the components of ` vec a` .

Explanation

To solve the problem, we need to find the acute angle \( \theta \) that the unit vector \( \vec{a} \) makes with the \( \hat{k} \) axis, and then determine the components of \( \vec{a} \).

### Step 1: Understanding the Angles
Given:
- The angle \( \alpha \) with \( \hat{i} \) (x-axis) is \( \frac{\pi}{3} \) (or 60 degrees).
- The angle \( \beta \) with \( \hat{j} \) (y-axis) is \( \frac{\pi}{4} \) (or 45 degrees).
- The angle \( \theta \) with \( \hat{k} \) (z-axis) is unknown.

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