Question

Explain why two nonparallel vectors and a point uniquely determine a plane containing both vectors and the point.

Short answer

A plane is determined by a point on the plane and two direction vectors and that are parallel to the plane.

Step-by-step solution

Step 1. Given Information

Explain why two nonparallel vectors and a point uniquely determine a plane containing both vectors and the point.

Step 2. Two nonparallel vectors and a point uniquely determine a plane containing both vectors and the point. 

A plane, apart from a line, does not have a clear "direction." However, there is a very useful way to connect a plane with a direction: there are exactly two directions perpendicular to a plane. The term "normal to the plane" refers to any vector that has one of these two directions. While a plane may have several normal vectors, they are almost all parallel or anti-parallel to one another.

A plane is defined by a point on the plane and two parallel direction vectors. The reason that we require two parallel vectors parallel to the plane instead of one for the line indicates that the plane is two dimensional while the line is one.