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. **Representation of Vector \( \vec{a} \)**:
Let \( \vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \).
Since \( |\vec{a}| = 2 \), we have:
\[
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