Three vectors are written as follows:
`vecA=-hati+2hatj+3hatk`
`vecB=2hati+3hatj-2hatk`
`vecC=5hati+nhatj+hatk`
What should be the value of a so that three vectors are coplanar ?

Explanation

To determine the value of \( n \) such that the vectors \( \vec{A} \), \( \vec{B} \), and \( \vec{C} \) are coplanar, we can use the condition that the scalar triple product of the vectors must be zero. This can be expressed in terms of a determinant.

The vectors are given as:
\[ \vec{A} = -\hat{i} + 2\hat{j} + 3\hat{k} \]
\[
\vec{B} = 2\hat{i} + 3\hat{j} - 2\hat{k}
...