If the magnitude of the sum of two vectors is | vedclass

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

Question

(A) Let the two vectors be $\vec{A}$ and $\vec{B}$.The magnitude of the sum of $\vec{A}$ and $\vec{B}$ is given by: $|\vec{A} + \vec{B}| = \sqrt{A^2 +

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) Let the two vectors be $\vec{A}$ and $\vec{B}$.The magnitude of the sum of $\vec{A}$ and $\vec{B}$ is given by: $|\vec{A} + \vec{B}| = \sqrt{A^2 + B^2 + 2AB \cos 	heta}$.The magnitude of the difference of $\vec{A}$ and $\vec{B}$ is given by: $|\vec{A} - \vec{B}| = \sqrt{A^2 + B^2 - 2AB \cos 	heta}$.Given that $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$,we square both sides:$A^2 + B^2 + 2AB \cos 	heta = A^2 + B^2 - 2AB \cos 	heta$.Subtracting $A^2 + B^2$ from both sides,we get:$2AB \cos 	heta = -2AB \cos 	heta$.$4AB \cos 	heta = 0$.Since $A$ and $B$ are non-zero vectors,$4AB 
eq 0$,therefore $\cos 	heta = 0$.This implies $	heta = 90^o$.

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 ........ $^o$.

Similar Questions

$A$ car moves with a speed of $20 \, m/s$ towards the North. It turns and moves with the same speed towards the West. What is the change in velocity?

If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,then the magnitude and direction of $\overrightarrow A + \overrightarrow B$ will be:

If $\vec{P}+\vec{Q}=\vec{P}-\vec{Q}$,then

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ has a magnitude $R_{1}$. If the direction of $\overrightarrow{Q}$ is reversed,the resultant has a magnitude $R_{2}$. The value of $(R_{1}^{2} + R_{2}^{2})$ is:

The sum of the magnitudes of two forces is $25 \,N$. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $10 \,N$. The two forces are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module