If `bar(a),bar(b),bar(c)` are non - coplanar vectors, then show the vectors `-bar(a)+3bar(b)-5bar(c),-bar(a)+bar(b)+bar(c)` and `2bar(a)-3bar(b)+bar(c)` are coplanar.

Explanation

To show that the vectors \(-\bar{a} + 3\bar{b} - 5\bar{c}\), \(-\bar{a} + \bar{b} + \bar{c}\), and \(2\bar{a} - 3\bar{b} + \bar{c}\) are coplanar, we can use the concept of the scalar triple product. If the scalar triple product of three vectors is zero, then the vectors are coplanar.

### Step 1: Define the vectors
Let:
\[ \bar{u} = -\bar{a} + 3\bar{b} - 5\bar{c} \]
\[
...