Question

Explain why a single nonzero vector and a point uniquely determine a plane containing the point. (Hint: Think of the collection of vectors orthogonal to the given vector with the given point as the initial point of all of the vectors.)

Short answer

A single nonzero vector and a point uniquely determine a plane containing the point if a given vector is a orthogonal to a plane.

Step-by-step solution

Step 1. Given Information

Explain why a single nonzero vector and a point uniquely determine a plane containing the point.

Step 2. A nonzero vector is one whose magnitude is greater than zero. 

If a given vector is orthogonal to a plane, a single nonzero vector and a point uniquely identify a plane containing the point.

If two vectors are perpendicular to each other, they are orthogonal. The dot product of the two vectors, in other words, is zero.