If `veca=7hati-4hatj-4hatk and vecb=-2hati-hatj+2hatk`, determine vector `vecc` along the internal bisector of the angle between vectors `veca and vecb` such that `|vecc|= 5sqrt6`.

Explanation

To solve the problem, we need to find the vector \(\vec{c}\) along the internal bisector of the angle between the vectors \(\vec{a}\) and \(\vec{b}\) such that \(|\vec{c}| = 5\sqrt{6}\).

### Step 1: Define the vectors
Given:
\[ \vec{a} = 7\hat{i} - 4\hat{j} - 4\hat{k} \]
\[
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