Which of the following relations is true for | vedclass

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

Question

(B) For two unit vectors $\hat{A}$ and $\hat{B}$ with angle $	heta$ between them:$|\hat{A}+\hat{B}| = \sqrt{|\hat{A}|^2 + |\hat{B}|^2 + 2|\hat{A}||\h

Vedclass · Accepted Answer

$|\hat{A}-\hat{B}|=|\hat{A}+\hat{B}| 	an \frac{	heta}{2}$

Vedclass · Answer

(B) For two unit vectors $\hat{A}$ and $\hat{B}$ with angle $	heta$ between them:$|\hat{A}+\hat{B}| = \sqrt{|\hat{A}|^2 + |\hat{B}|^2 + 2|\hat{A}||\hat{B}| \cos 	heta} = \sqrt{1+1+2 \cos 	heta} = \sqrt{2(1+\cos 	heta)} = \sqrt{2(2 \cos^2 \frac{	heta}{2})} = 2 \cos \frac{	heta}{2}$.$|\hat{A}-\hat{B}| = \sqrt{|\hat{A}|^2 + |\hat{B}|^2 - 2|\hat{A}||\hat{B}| \cos 	heta} = \sqrt{1+1-2 \cos 	heta} = \sqrt{2(1-\cos 	heta)} = \sqrt{2(2 \sin^2 \frac{	heta}{2})} = 2 \sin \frac{	heta}{2}$.Dividing the two magnitudes:$\frac{|\hat{A}-\hat{B}|}{|\hat{A}+\hat{B}|} = \frac{2 \sin \frac{	heta}{2}}{2 \cos \frac{	heta}{2}} = 	an \frac{	heta}{2}$.Therefore,$|\hat{A}-\hat{B}| = |\hat{A}+\hat{B}| 	an \frac{	heta}{2}$.

Column $-I$	Column $-II$
$(a) \vec a + \vec b = \vec c$	$(i)$ Vector $\vec a$ is along $+Y$,$\vec c$ is along $+X$,and $\vec b$ connects the origin to the tip of $\vec c$
$(b) \vec a - \vec c = \vec b$	$(ii)$ Vector $\vec a$ is along $+X$,$\vec b$ is along $+Y$,and $\vec c$ connects the origin to the tip of $\vec b$
$(c) \vec b - \vec a = \vec c$	$(iii)$ Vector $\vec c$ is along $+X$,$\vec a$ is along $+Y$,and $\vec b$ connects the tip of $\vec c$ to the tip of $\vec a$
$(d) \vec a + \vec b + \vec c = 0$	$(iv)$ Vector $\vec a$ is along $-X$,$\vec b$ is along $-Y$,and $\vec c$ connects the origin to the tip of $\vec b$

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

Similar Questions

$A$ car travels $6 \, km$ at an angle of $45^o$ north of east and then travels a distance of $4 \, km$ at an angle of $135^o$ north of east. How far is the final point from the starting point? What angle does the straight line joining its initial and final position make with the east direction?

If the sum of two unit vectors is also a unit vector,then the magnitude of their difference and the angle between the two given unit vectors is ..............

The vectors $5\hat{i} + 8\hat{j}$ and $2\hat{i} + 7\hat{j}$ are added. The magnitude of the sum of these vectors is

If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,find the magnitude and direction of $\overrightarrow A + \overrightarrow B$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module