If in parallelogram ABCD, diagonal vectors are `vec(AC)=2hati+3hatj+4hatk` and `vec(BD)=-6hati+7hatj-2hatk`, then find the adjacent side vectors `vec(AB) and vec(AD)`.

Explanation

To solve the problem, we need to find the vectors \(\vec{AB}\) and \(\vec{AD}\) given the diagonal vectors \(\vec{AC}\) and \(\vec{BD}\) of the parallelogram ABCD.

### Step 1: Write down the given vectors
We have:
\[ \vec{AC} = 2\hat{i} + 3\hat{j} + 4\hat{k} \]
\[
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