What is a unit vector? Explain.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) vector whose magnitude is $1$ unit is called a unit vector.
It represents the direction of a vector.
It does not have any unit or dimensions.
In a Cartesian coordinate system,the unit vectors along the $x, y,$ and $z$ axes are denoted by $\hat{i}, \hat{j},$ and $\hat{k}$ respectively.
Since the magnitude of a unit vector is $1$,we have:
$|\hat{i}| = |\hat{j}| = |\hat{k}| = 1$
These vectors are mutually perpendicular to each other.
$A$ unit vector can be obtained by dividing a vector by its magnitude.
Example: If the unit vector of $\vec{A}$ is $\hat{n}$,then:
$\hat{n} = \frac{\vec{A}}{|\vec{A}|} = \frac{\vec{A}}{A} = \frac{\text{vector}}{\text{magnitude of vector}}$
According to this equation,$\vec{A} = |\vec{A}| \cdot \hat{n}$
Vector $=$ (Magnitude of vector) $\times$ (Its unit vector)
Example: $A$ force of $5 \text{ N}$ acting along the $X$-axis can be represented as: $\vec{F} = 5\hat{i} \text{ N}$.

Explore More

Similar Questions

Match Column $-I$ with Column $-II$.
Column $-I$ Column $-II$
$(1)$ Angular momentum $(a)$ Scalar
$(2)$ Potential energy $(b)$ Vector
$(c)$ Unit vector

If $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is ........ $^\circ$.

$A$ vector makes $45^{\circ}$ and $60^{\circ}$ angles with the $x$ and $y$ axes respectively. The unit vector along the given vector is:

Difficult
View Solution

The figure shows $ABCDEF$ as a regular hexagon. What is the value of $\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF}$ in terms of $\overrightarrow {AO}$?

Difficult
View Solution

Given $\vec{P} + \vec{Q} = \vec{P} - \vec{Q}$. Under what condition is this true?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo