Show that the vectors ` vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k` are coplanar.

Explanation

To show that the vectors \( \vec{a} = -2 \hat{i} - 2 \hat{j} + 4 \hat{k} \), \( \vec{b} = -2 \hat{i} + 4 \hat{j} - 2 \hat{k} \), and \( \vec{c} = 4 \hat{i} - 2 \hat{j} - 2 \hat{k} \) are coplanar, we can use the concept that three vectors are coplanar if one of them can be expressed as a linear combination of the other two.

### Step-by-step Solution

1. **Write the vectors**:
\[ \vec{a} = -2 \hat{i} - 2 \hat{j} + 4 \hat{k} \]
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