MCQ
The value of a unit vector in the direction of vector $A = 5\hat i - 12\hat j,$ is
- A$\hat i$
- B$\hat j$
- C$(\hat i + \hat j)/13$
- ✓$(5\hat i - 12\hat j)/13$
✓
Answer
Correct option: D.
$(5\hat i - 12\hat j)/13$
d
(d) $\vec A = 5\hat i + 12\hat j$,$|\vec A| = \sqrt {{5^2} + {{( - 12)}^2}} $=$\sqrt {25 + 144} $$ = 13$
(d) $\vec A = 5\hat i + 12\hat j$,$|\vec A| = \sqrt {{5^2} + {{( - 12)}^2}} $=$\sqrt {25 + 144} $$ = 13$
Unit vector $\hat A = \frac{{\vec A}}{{|\vec A|}}$=$\frac{{5\hat i - 12\hat j}}{{13}}$
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 area of the plates of a parallel plate capacitor is $A$ and the gap between them is $d$. The gap is filled with a non-homogeneous dielectric whose dielectric constant varies with the distance $‘y’$ from one plate as : $K = \lambda \ sec(\pi y/2d)$, where $\lambda $ is a dimensionless constant. The capacitance of this capacitor is
→major product
A metal ball of surface area $200\;c{m^2}$ and temperature ${527^o}C$ is surrounded by a vessel at ${27^o}C$. If the emissivity of the metal is $0.4$ , then the rate of loss of heat from the ball is .......... $joules $ approx. $(\sigma = 5.67 \times {10^{ - 8}}J/{m^2}\; - s - {k^4})$
→A bomber plane moves horizontally with a speed of $500\,m/s$ and a bomb released from it, strikes the ground in $10\,sec$. Angle with horizontal at which it strikes the ground will be $(g = 10\,m/s^2)$
→The frequency of a sound wave is $n$ and its velocity is $v$. If the frequency is increased to $4n,$ the velocity of the wave will be
→When an air column at $15\,^oC$ and a tunning fork are sounded together then $4$ beats per second are produced, the frequency of the fork is less then that of air column. When the temperature falls to $10\,^oC$ , then the beat frequency decreases by one. The frequency of the fork will be ..... $Hz$ $[V_{sound}$ at $0\,^oC = 332\,m/s]$
→If a magnet of length $10 \,cm $ and pole strength $ 40 \,A-m$ is placed at an angle of $45^o$ in an uniform induction field of intensity $2 \times 10^{-4}\, T$, the couple acting on it is
→The magnetic field in the cylindrical region shown in figure increases at a constant rate of $20\, mT/sec$. Each side of the square loop $ABCD$ has a length of $1\, cm$ and resistance of $4 \Omega$. Find the current in the wire $AB$ if the switch $S$ is closed
→An electron initially at rest, is accelerated through a potential difference of $ 200$ volt, so that it acquires a velocity $8.4 \times {10^6}m/s.$ The value of $e/m$ of electron will be
→The electric field $E$, current density $J$ and conductivity $\sigma$ of a conductor are related as
→