Vectors `2hati+2hatj-2hatk,5hati+yhatj+hatk and -hati+2hatj+2hatk` are coplanar then find the value of y.

Explanation

To determine the value of \( y \) such that the vectors \( \vec{A} = 2\hat{i} + 2\hat{j} - 2\hat{k} \), \( \vec{B} = 5\hat{i} + y\hat{j} + \hat{k} \), and \( \vec{C} = -\hat{i} + 2\hat{j} + 2\hat{k} \) are coplanar, we can use the concept of the scalar triple product. The vectors are coplanar if their scalar triple product (or box product) is equal to zero.

### Step-by-Step Solution:

1. **Write the vectors:**
\[ \vec{A} = 2\hat{i} + 2\hat{j} - 2\hat{k} \]
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