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 \( \vec{c} \), and to find the angle, we can follow these steps:

### Step 1: Define the Magnitudes
Let the magnitudes of the vectors \( \vec{a}, \vec{b}, \) and \( \vec{c} \) be \( \lambda \). Since they are mutually perpendicular, we have:
\[ |\vec{a}| = |\vec{b}| = |\vec{c}| = \lambda \]

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