If ` -> a , -> b , -> c`are mutually perpendicular vectors of equal magnitudes, show that the vector ` -> a+ -> b+ -> c`is equally inclined to ` -> a , -> b`and ` -> c`.

Explanation

To show that the vector \( \vec{a} + \vec{b} + \vec{c} \) is equally inclined to the vectors \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \), we will follow these steps:

### Step 1: Understand the Given Information
We know that \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \) are mutually perpendicular vectors of equal magnitudes. This means:
- \( \vec{a} \cdot \vec{b} = 0 \)
- \( \vec{b} \cdot \vec{c} = 0 \)
- \( \vec{c} \cdot \vec{a} = 0 \)
- \( |\vec{a}| = |\vec{b}| = |\vec{c}| \)
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