# Coplanar

Two or more vectors are coplanar if they are linearly dependent, therefore their components are proportional and the rank is 2.

Two or more points are coplanar if the vectors determined by them are also coplanar.

#### Examples

1. Determine if the points A = (1, 2, 3), B = (4, ,7, 8), C = (3, 5, 5), D = (−1, −2, −3) and E = (2, 2, 2) are coplanar.

The points A, B, C, D and E are coplanar if:

The points A, B, C, D and E are not coplanar.

2.Calculate the value of **x** for the coplanar set of points A = (0, 0, 1), B = (0, 1, 2), C = (−2, 1, 3) and D = (x, x−1, 2).

3.What are the values of a, b and c so that the points A = (1, 0, 1), B = (1, 1, 0), C = (0, 1, 1) and D = (a, b, c) are coplanar?

The points A, B, C and D are coplanar if:

4.Calculate the value of **a** for the points (a, 0, 1), (0, 1, 2), (1, 2, 3) and (7, 2, 1) so that they are coplanar. Also, calculate the equation of the plane that contains them.