If the projections of vector ` vec a` on `x` -, `y` - and `z` -axes are 2, 1 and 2 units ,respectively, find the angle at which vector ` vec a` is inclined to the `z` -axis.

Explanation

To find the angle at which the vector \( \vec{a} \) is inclined to the z-axis given its projections on the x, y, and z axes, we can follow these steps:

### Step 1: Write the vector in component form
Given the projections of vector \( \vec{a} \) on the x, y, and z axes are 2, 1, and 2 units respectively, we can express the vector \( \vec{a} \) in component form:
\[ \vec{a} = 2\hat{i} + 1\hat{j} + 2\hat{k} \]

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