The magnitude of the sum of the two vectors v | vedclass

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

Question

(C) Let the two vectors be $\vec{A}$ and $\vec{B}$ with magnitudes $A$ and $B$ respectively.The magnitude of their sum is given by:$|\vec{A}+\vec{B}|

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(C) Let the two vectors be $\vec{A}$ and $\vec{B}$ with magnitudes $A$ and $B$ respectively.The magnitude of their sum is given by:$|\vec{A}+\vec{B}| = \sqrt{A^{2}+B^{2}+2AB \cos 	heta}$,where $	heta$ is the angle between the vectors.The magnitude of their difference 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 magnitudes of vectors,$A 
eq 0$ and $B 
eq 0$,therefore $\cos 	heta = 0$.This implies $	heta = 90^{\circ}$.

The magnitude of the sum of the two vectors $\vec{A}$ and $\vec{B}$ is equal to the magnitude of the difference of the two vectors $\vec{A}$ and $\vec{B}$. The angle between $\vec{A}$ and $\vec{B}$ is: (in $^{\circ}$)

Similar Questions

If $|\vec{a}|=2$ and $|\vec{b}|=3$,find the value of $|3 \vec{a}+2 \vec{b}|$ based on the given figure.

If $\overrightarrow{R}$ is the resultant vector of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$,then $|\overrightarrow{R}|$ is . . . . . . $|\overrightarrow{A}| + |\overrightarrow{B}|$.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled,the new resultant vector becomes perpendicular to $\vec{A}$. Then the magnitude of $\vec{C}$ is

Two forces of magnitude $F$ have a resultant of the same magnitude $F$. The angle between the two forces is ........ $^o$

If the resultant vector of vectors $\vec{A} = 4\hat{i} + 3\hat{j} + 6\hat{k}$ and $\vec{B} = -\hat{i} + 3\hat{j} - 8\hat{k}$ is parallel to a unit vector,then $\vec{R}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module