Question

$\overrightarrow{A}$ is a vector with magnitude $A$, then the unit vector $\hat{A}$ in the direction of $\overrightarrow{A}$ is

• A. $A\overrightarrow{A}$
• B. $\overrightarrow{A}.\overrightarrow{A}$
• C. $\overrightarrow{A}\times \overrightarrow{A}$
• D. $\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$

Answer 1

The correct option is D

$\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$

Explanation for the correct option(s):

D: $\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$

We know that,

Unit vector is a quantity that has both magnitude, as well as direction and which has a magnitude of 1.

Mathematically express as: $\hat{A}=\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$

Explanation for the incorrect option(s):

A: $A\overrightarrow{A}$

Product of magnitude and vector is a vector,

B:.$\overrightarrow{A}.\overrightarrow{A}$

Dot product

C: $\overrightarrow{A}\times \overrightarrow{A}$

Cross product

Hence, the unit vector $\hat{A}$ in the direction of $\overrightarrow{A}$ is $\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$