MCQ
The angle made by the vector $\left( {\hat i\,\, + \;\,\hat j} \right)$ with $x-$ axis and $y$ axis is
- A$45^o, 60^o$
- B$60^o, 60^o$
- ✓$45^o, 45^o$
- D$60^o, 45^o$
✓
Answer
Correct option: C.
$45^o, 45^o$
c
$a = \sqrt {{a_x}^2\,\, + \;\,{a_y}^2} = \sqrt {{1^2} + \;\,{1^2}} = \sqrt 2$
$a = \sqrt {{a_x}^2\,\, + \;\,{a_y}^2} = \sqrt {{1^2} + \;\,{1^2}} = \sqrt 2$
$\cos \alpha = \frac{{{a_x}}}{a} = \frac{1}{{\sqrt 2 }}$
$\therefore \alpha = 45^\circ ;\,\cos \,\beta = \frac{{{a_y}}}{a} = \frac{1}{{\sqrt 2 }}$
$\therefore \beta = 45^\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
What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of $150 \,{km}$ ? The average population density around the tower is $2000 \,/ {km}^{2}$ and the value of ${R}_{{e}}=6.5 \times 10\, {m}$
→A wheel is rolling straight on ground without slipping. If the axis of the wheel has speed $v$, the instantenous velocity of a point $P$ on the rim, defined by angle $\theta $, relative to the ground will be
→A particle moves along $X$-axis from $x=0$ to $x=1 \,m$ under the influence of a force given by $F=3 x^2+2 x-10$. Work done in the process is ............. $J$
→A cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. ....... $kg$ is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water $= 10^3\,kg/m^3$ ]
→$A \,10\, kg$ ball attached to the end of a rigid massless rod of length $1\, m$ rotates at constant speed in a horizontal circle of radius $0.5\, m$ and period $1.57 \, sec$ as in fig. The force exerted by rod on the ball is ........ $N$.
→A coil having an area $2\,{m^2}$ is placed in a magnetic field which changes from $1\,Wb/{m^2}$ to $4\,Wb/{m^2}$ in a interval of $2$ second. The $e.m.f.$ induced in the coil will be......$V$
→In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius $0.5 \times 10^{-10}\,m$. If the speed of electron is $2.2 \times 10^{6} \;{m} / {s}$, then the current associated with the electron will be $....\,\times 10^{-2} \;{mA}$. [Take $\pi$ as $\left.\frac{22}{7}\right]$
→A $12.5\, eV$ electron beam is used to bombard gaseous hydrogen at room temperature. It will emit
→The work done to take an electron from rest where potential is $-60\, V$ to another point where potential is $-20\, V$ is given by.....$eV$
→A parallel plate capacitor is formed by two plates each of area $30 \pi\, cm ^{2}$ separated by $1\, mm$. A material of dielectric strength $3.6 \times 10^{7} \,Vm ^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6}\, C$, the value of dielectric constant of the material is
→$\left\{ Use : \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right\}$