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

Explanation

To find the value of the acute angle \( \theta \) that the unit vector \( \vec{a} \) makes with the \( \hat{k} \) axis, we can follow these steps:

### Step 1: Understand the Direction Cosines
The direction cosines of a unit vector are given by the cosines of the angles it makes with the coordinate axes. Let:
- \( \alpha \) be the angle with \( \hat{i} \) (x-axis),
- \( \beta \) be the angle with \( \hat{j} \) (y-axis),
- \( \gamma \) be the angle with \( \hat{k} \) (z-axis).

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