Show that the four points A, B, C and D with position vectors respectively are coplanar.
Given position vectors of four points A, B, C and D are:
These points are coplanar, if the vectors, are coplanar.
These vectors are coplanar if and only if, they can be expressed as a linear combination of other two.
So Let
Comparing the coefficients, we have,
These values of x and y satisfy the equation 3x + 3y = -2.
Hence the vectors are coplanar.