Which of the following relations is true for two unit vectors $\hat{ A }$ and $\hat{ B }$ making an angle $\theta$ to each other$?$
Which of the following relations is true for two unit vectors $\hat{ A }$ and $\hat{ B }$ making an angle $\theta$ to each other$?$
- [JEE MAIN 2022]
- A
$|\hat{ A }+\hat{ B }|=|\hat{ A }-\hat{ B }| \tan \frac{\theta}{2}$
- B
$|\hat{ A }-\hat{ B }|=|\hat{ A }+\hat{ B }| \tan \frac{\theta}{2}$
- C
$|\hat{ A }+\hat{ B }|=|\hat{ A }-\hat{ B }| \cos \frac{\theta}{2}$
- D
$|\overrightarrow{ A }-\hat{ B }|=|\overrightarrow{ A }+\hat{ B }| \cos \frac{\theta}{2}$
Similar Questions
Two forces $F_1 = 3N$ at $0^o$ and $F_2 = 5N$ at $60^o$ act on a body. Then a single force that would balance the two forces must have a magnitude of .......... $N$
Two forces $F_1 = 3N$ at $0^o$ and $F_2 = 5N$ at $60^o$ act on a body. Then a single force that would balance the two forces must have a magnitude of .......... $N$
Two vectors $\dot{A}$ and $\dot{B}$ are defined as $\dot{A}=a \hat{i}$ and $\overrightarrow{\mathrm{B}}=\mathrm{a}(\cos \omega t \hat{\mathrm{i}}+\sin \omega t \hat{j}$ ), where a is a constant and $\omega=\pi / 6 \mathrm{rad} \mathrm{s}^{-1}$. If $|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{3}|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|$ at time $t=\tau$ for the first time, the value of $\tau$, in, seconds, is. . . . . .
Two vectors $\dot{A}$ and $\dot{B}$ are defined as $\dot{A}=a \hat{i}$ and $\overrightarrow{\mathrm{B}}=\mathrm{a}(\cos \omega t \hat{\mathrm{i}}+\sin \omega t \hat{j}$ ), where a is a constant and $\omega=\pi / 6 \mathrm{rad} \mathrm{s}^{-1}$. If $|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{3}|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|$ at time $t=\tau$ for the first time, the value of $\tau$, in, seconds, is. . . . . .
- [IIT 2018]
Two forces with equal magnitudes $F$ act on a body and the magnitude of the resultant force is $F/3$. The angle between the two forces is
Two forces with equal magnitudes $F$ act on a body and the magnitude of the resultant force is $F/3$. The angle between the two forces is
Two vectors $\vec A\,{\rm{ and }}\vec B$ are such that $\vec A + \vec B = \vec A - \vec B$. Then
Three vectors $\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$ and $\overrightarrow{\mathrm{OR}}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A \sqrt{x}$. The value of $x$ is. . . . . . . . .
Three vectors $\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$ and $\overrightarrow{\mathrm{OR}}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A \sqrt{x}$. The value of $x$ is. . . . . . . . .
- [JEE MAIN 2024]