Two vectors having equal magnitudes A make an | vedclass

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

Question

(A) Let the two vectors be $\vec{P}$ and $\vec{Q}$ such that $|\vec{P}| = |\vec{Q}| = A$.The magnitude of the resultant vector $\vec{R} = \vec{P} + \v

Vedclass · Accepted Answer

$2\,A \cos \frac{	heta}{2}$,along bisector

Vedclass · Answer

(A) Let the two vectors be $\vec{P}$ and $\vec{Q}$ such that $|\vec{P}| = |\vec{Q}| = A$.The magnitude of the resultant vector $\vec{R} = \vec{P} + \vec{Q}$ is given by $R = \sqrt{P^2 + Q^2 + 2PQ \cos 	heta}$.Substituting the values,we get $R = \sqrt{A^2 + A^2 + 2A^2 \cos 	heta} = \sqrt{2A^2(1 + \cos 	heta)}$.Using the trigonometric identity $1 + \cos 	heta = 2 \cos^2 \frac{	heta}{2}$,we get $R = \sqrt{2A^2 \cdot 2 \cos^2 \frac{	heta}{2}} = \sqrt{4A^2 \cos^2 \frac{	heta}{2}} = 2A \cos \frac{	heta}{2}$.Since the magnitudes of the two vectors are equal,the resultant vector bisects the angle between them. Thus,the direction is along the angle bisector.

Two vectors having equal magnitudes $A$ make an angle $\theta$ with each other. The magnitude and direction of the resultant are respectively

Similar Questions

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

Two vectors of equal magnitude $5$ units have an angle $60^\circ$ between them. Find the magnitude of $(a)$ the sum of the vectors and $(b)$ the difference of the vectors.

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors,the angle between these vectors is ........ $^o$.

Which of the following relations is true for two unit vectors $\hat{A}$ and $\hat{B}$ making an angle $\theta$ to each other?

If $\vec{a}$ and $\vec{b}$ are two unit vectors inclined at an angle of $60^{\circ}$ to each other,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module