MCQ
$\vec A$ and $\vec B$ are two vectors and $\theta$ is the angle between them, if $|\vec A \times \vec B|=\sqrt 3(\vec A \cdot \vec B) $ the value of $\theta$ is ......... $^o$
- ✓$60$
- B$45$
- C$180$
- D$0$
✓
Answer
Correct option: A.
$60$
a
$\left| {\vec A \times \vec B} \right| = \sqrt 3 \left( {\vec A \cdot \vec B} \right)$
$\left| {\vec A \times \vec B} \right| = \sqrt 3 \left( {\vec A \cdot \vec B} \right)$
$AB\sin \theta = \sqrt 3 AB\cos \theta$
$\tan \theta = \sqrt 3$
$\theta = {\tan ^{ - 1}}\sqrt 3 = {60^ \circ }$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The diagram shows a force-extension graph for a rubber band. Consider the following statements
→$I.$ It will be easier to compress this rubber than expand it
$II.$ Rubber does not return to its original length after it is stretched
$III.$ The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph
Four rods of silver, copper, brass and wood are of same shape. They are heated together after wrapping a paper on it, the paper will burn first on
Mercury does not wet glass, wood or iron because
The dimensions of $\frac{\alpha}{\beta}$ in the equation $F=\frac{\alpha-t^2}{\beta v^2}$, where $F$ is the force, $v$ is velocity and $t$ is time, is ..........
→A wave disturbance in a medium is described by $y(x,\,t) = 0.02\cos \,\left( {50\,\pi t + \frac{\pi }{2}} \right)\cos (10\pi x)$, where $ x$ and $y$ are in metres and $t$ in seconds
→Small water droplets of radius $0.01 \mathrm{~mm}$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$. Due to condensation, if $8 \mathrm{such}$ droplets are coalesced and formed a larger drop, the new terminal velocity will be ........... $\mathrm{cm} / \mathrm{s}$.
→The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\ C$ and $210^o\ C$, the rate of heat flow will be.... $J/s$
→A black body of surface area $10cm^2$ is heated to $127°C$ and is suspended in a room at temperature $27°C$ . The initial rate of loss of heat from the body at the room temperature will be ...... $W$
→A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
→The variation of the acceleration $a$ of the particle executing $S.H.M.$ with displacement $x$ is as shown in the figure
→