If ` veca , vecb , vecc`are mutually perpendicular vectors of equal magnitudes, show that the vector ` veca+ vec b+ vec c`is equally inclined to ` vec a , vec b` and ` vec 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: Define the Magnitudes of the Vectors
Let the magnitudes of the vectors \( \vec{a}, \vec{b}, \) and \( \vec{c} \) be equal to \( x \). Thus, we have:
\[ |\vec{a}| = |\vec{b}| = |\vec{c}| = x \]

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