If ` vec a ,\ vec b ,\ vec c` are three mutually perpendicular vectors of equal magniltgude, prove that ` vec a+ vec b+ vec c` is equally inclined with vectors ` vec a ,\ vec b ,\ a n d\ vec cdot` also find the angle.

Explanation

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

### Step 1: Understand the properties of the vectors
Given that \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are mutually perpendicular vectors of equal magnitude, we can denote their magnitudes as:
\[ |\vec{a}| = |\vec{b}| = |\vec{c}| = \lambda \]

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