A vector of length ell is turned by an angle | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the initial vector be $\vec{\ell}_1$ and the final vector be $\vec{\ell}_2$. Both have magnitude $\ell$,so $|\vec{\ell}_1| = |\vec{\ell}_2| =

Vedclass · Accepted Answer

$2\ell \sin \frac{	heta}{2}$

Vedclass · Answer

(B) Let the initial vector be $\vec{\ell}_1$ and the final vector be $\vec{\ell}_2$. Both have magnitude $\ell$,so $|\vec{\ell}_1| = |\vec{\ell}_2| = \ell$.The change in the position vector of the tip is given by $\Delta \vec{\ell} = \vec{\ell}_2 - \vec{\ell}_1$.The magnitude of the change is $|\Delta \vec{\ell}| = \sqrt{|\vec{\ell}_2|^2 + |\vec{\ell}_1|^2 - 2|\vec{\ell}_2||\vec{\ell}_1| \cos 	heta}$.Substituting the magnitudes,we get $|\Delta \vec{\ell}| = \sqrt{\ell^2 + \ell^2 - 2\ell^2 \cos 	heta}$.$|\Delta \vec{\ell}| = \sqrt{2\ell^2(1 - \cos 	heta)}$.Using the trigonometric identity $1 - \cos 	heta = 2 \sin^2 \frac{	heta}{2}$,we get:$|\Delta \vec{\ell}| = \sqrt{2\ell^2 \cdot 2 \sin^2 \frac{	heta}{2}} = \sqrt{4\ell^2 \sin^2 \frac{	heta}{2}}$.$|\Delta \vec{\ell}| = 2\ell \sin \frac{	heta}{2}$.

$A$ vector of length $\ell$ is turned by an angle $\theta$. Find the change in the position vector of the tip.

Similar Questions

If two forces of equal magnitudes act simultaneously on a body in the east and the north directions,then:

Two vectors having equal magnitudes of $x$ units acting at an angle of $45^\circ$ have a resultant of $\sqrt{2 + \sqrt{2}}$ units. The value of $x$ is

Let the two forces have equal magnitude $A$. If the magnitude of the resultant is $\frac{2A}{3}$,then the angle between those two forces is:

If $|A|=2$ and $|B|=4$ and the angle between them is $60^{\circ}$,then $|A-B|$ is

The sum of two forces $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$ such that $|\overrightarrow{R}| = |\overrightarrow{P}|$. The angle $\alpha$ (in degrees) that the resultant of $2\overrightarrow{P}$ and $\overrightarrow{Q}$ will make with $\overrightarrow{Q}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module