Suggested languages for you:

Americas

Europe

Q. 1

Expert-verifiedFound in: Page 879

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

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

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

It is given that **v **is a non-zero vector.

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

94% of StudySmarter users get better grades.

Sign up for free