Question

Unit vectors: If v is a nonzero vector, explain why $\frac{\mathbf{v}}{\left|\left|v\right|\right|}$ is a unit vector.

Short answer

By definition of a unit vector if v is a nonzero vector then $\frac{\mathbf{v}}{||v||}$is a unit vector.

Step-by-step solution

Step 1. Given Information.

It is given thatvis a non-zero vector.

Step 2. Explanation.

A unit vector is defined as the vector that has a magnitude equal to $1$and its formula is $\overrightarrow{u}=\frac{v}{||v||}.$

If v is a non-zero vector and we divide it by its magnitude, then by the definition of a unit vector it is also a unit vector.

Thus, $\frac{v}{\left|\left|v\right|\right|}=\overrightarrow{u}.$