If ` |veca|=2` then find the value of `|vecaxxveci|^(2)+|vecaxxvecj|^(2)+|vecaxxveck|^2`

Explanation

To solve the problem, we need to find the value of \( |\vec{a} \times \vec{i}|^2 + |\vec{a} \times \vec{j}|^2 + |\vec{a} \times \vec{k}|^2 \) given that \( |\vec{a}| = 2 \).

### Step-by-Step Solution:

1. **Understanding the Cross Product**:
The cross product of two vectors \(\vec{a}\) and \(\vec{b}\) can be calculated using the determinant of a matrix formed by the unit vectors and the components of the vectors. For \(\vec{a} = (a_1, a_2, a_3)\), the cross products with the unit vectors \(\vec{i}, \vec{j}, \vec{k}\) will yield vectors perpendicular to \(\vec{a}\).

2. **Calculate \(|\vec{a} \times \vec{i}|^2\)**:
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