MCQ
The expression $\left( {\frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat j} \right)$ is a
- ✓Unit vector
- BNull vector
- CVector of magnitude $\sqrt 2 $
- DScalar
✓
Answer
Correct option: A.
Unit vector
a
(a) $\vec P = \frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat j$
(a) $\vec P = \frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat j$
$|\vec P| = \sqrt {{{\left( {\frac{1}{{\sqrt 2 }}} \right)}^2} + {{\left( {\frac{1}{{\sqrt 2 }}} \right)}^2}} = 1$
It is a unit vector.
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 fundamental frequency of a closed pipe is $220 Hz$. If $\frac{1}{4}$ of the pipe is filled with water, the frequency of the first overtone of the pipe now is ..... $Hz$
→For one complete cycle of a thermodynamic processes on a gas as shown in $P-V$ diagram. Which is true
→Water is moving with a speed of $5.18 ms^{-1}$ through a pipe with a cross-sectional area of $4.20 cm^2$. The water gradually descends $ 9.66 m $ as the pipe increase in area to $7.60 cm^2$. The speed of flow at the lower level is ....... $ms^{-1}$
→For a thermodynamic process $\delta Q = -50$ $calorie$ and $W = -20$ $calorie$ . If the initial internal energy is $-30$ $calorie$ then final internal energy will be ....... $calorie$
→A very tall vertical cylinder is filled with a gas of molar mass $M$ under isothermal conditions at temperature $T.$ The density and pressure of the gas at the base of the container is $\rho_0$ and $p_0$, respectively Choose the correct statement $(s)$ if gravity is assumed to be constant throughout the container
→When we see an object, the image formed on the retina is:
The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is
Frequency of a sonometer wire is $n.$ Now its tension is increased $4$ times and its length is doubled then new frequency will be
→Work done by a system under isothermal change from a volume ${V_1}$ to ${V_2}$ for a gas which obeys Vander Waal's equation $(V - \beta n)\,\left( {P + \frac{{\alpha {n^2}}}{V}} \right) = nRT$
→A train is moving on a straight track with speed $20\ ms^{-1}$. It is blowing its whistle at the frequency of $1000\ Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is ( speed of sound $=320$ $ms^{-1}$ ) close to .... $\%$
→