If `veca,vecb and vecc` are three mutually perpendicular unit vectors and `vecd` is a unit vector which makes equal angle with `veca,vecb and vecc`, then find the value of `|veca+vecb+vecc+vecd|^(2)`.

Explanation

To solve the problem, we need to find the value of \(|\vec{a} + \vec{b} + \vec{c} + \vec{d}|^2\), where \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are mutually perpendicular unit vectors, and \(\vec{d}\) is a unit vector that makes equal angles with \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\).

### Step-by-Step Solution:

1. **Define the vectors:**
Let \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) be unit vectors along the x, y, and z axes respectively:
\[
\vec{a} = \hat{i}, \quad \vec{b} = \hat{j}, \quad \vec{c} = \hat{k}
...