If are non–coplanar vectors, prove that the following vectors are non–coplanar :

and

Vectors parallel to the same plane, or lie on the same plane are called coplanar vectors

The three vectors are coplanar if one of them is expressible as a linear combination of the other two.

We have been given that, , and .

We can form a relation using these three vectors. Say,

Compare the vectors , and . We get

2 = x + y …(1)

–1 = x + y …(2)

3 = –2x – 3y …(3)

Solving equations (1) and (2) for x and y.

Equation (1), x + y = 2

Equation (2), x + y = –1

We get

The value of x and y cannot be found so it won’t satisfy equation (3).

Thus, , and are not coplanar.