If the vectors `xhati+hatj+hatk,hati+yhatj+hatk and hati+hatj+zhatk` are coplanar where, `x ne1,y ne1 and z ne1`, then prove that
`(1)/(1-x)+(1)/(1-y)+(1)/(1-z)=1`

Explanation

To prove that the vectors \( \mathbf{a} = x \hat{i} + \hat{j} + \hat{k} \), \( \mathbf{b} = \hat{i} + y \hat{j} + \hat{k} \), and \( \mathbf{c} = \hat{i} + \hat{j} + z \hat{k} \) are coplanar, we need to show that the determinant of the matrix formed by these vectors is zero.

### Step-by-Step Solution:

1. **Set up the determinant**:
The vectors can be represented as a matrix:
\[
\begin{vmatrix}
...