MCQ
The angle between the vectors $(\hat i + \hat j)$ and $(\hat j + \hat k)$ is ....... $^o$
- A$30$
- B$45$
- ✓$60$
- D$90$
✓
Answer
Correct option: C.
$60$
c
(c) $(\hat i + \hat j).(\hat j + \hat k) = 0 + 0 + 1 + 0 = 1$
(c) $(\hat i + \hat j).(\hat j + \hat k) = 0 + 0 + 1 + 0 = 1$
$\cos \theta = \frac{{\vec A.\vec B}}{{|\vec A||\vec B|}} = \frac{1}{{\sqrt 2 \times \sqrt 2 }} = \frac{1}{2}$
$\theta = 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
Two satellite $A$ and $B$ go round a planet in circular orbits having radii $4 R$ and $R$ respectively. If the speed of $\mathrm{A}$ is $3 v$, the speed of $\mathrm{B}$ will be :
→A police car with a siren of frequency $8 \ kHz$ is moving with uniform velocity $36 \ km / hr$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \ m / s$. The frequency of the siren heard by the car driver is
→A horizontal beam is pivoted at $O$ as shown in the figure. Find the mass $m$ to make the scale straight ........ $kg.$
→A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is
→A moves with $65 \,km/h $ while $B$ is moving in same direction of $A$ with $80\, km/h$. The relative velocity of $B$ with respect to $A$ is......... $km/h$
→Let $\theta$ be the angle between vectors $\vec{A}$ and $\vec{B}$. Which of the following figures correctly represents the angle $\theta$ ?
→A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong
Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ are released in free space with initial separation between their centres equal to $12R.$ If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is
→Two cars are moving in the same direction with a speed of $30\ kph$ . They are separated from each other by $5\ km$ . Third car moving in the opposite direction meets the two cars after an interval of $4\ minutes$ . What is the speed of the third car ?..........$km/h$
→For an ideal gas, in an isothermal process