Let be a plane defined by the scalar parametric equations

- Determine which of the following points are on .
- Find vectors such that .

- The point is not on since
Then,

But then the first coordinate fails since

The point is on since the system of equations

has a solution . Therefore, for .

The point is on since the system of equations

has a solution .

- Since is on the plane we take . Then from the parametric equations we get the vectors and as the coordinates of and . So, and . Then we have