Question

Determine if the three vectors a = (1, 4, - 7)  b = (2, -1, 4) and vector c = (0, - 9,18)  lie in the same plane or not.

Answer 1

Three vectors lies in the same plane if volume of the parallelepiped formed by these three vectors is zero.

So, as we noted prior to this example all we need to do is compute the volume of the parallelepiped formed by these three vectors. If the volume is zero, then they lie in the same plane and if the volume isn’t zero they don’t lie in the same plane.

So, the volume is zero and so they lie in the same plane.