Question
The angle between two vectors $ - 2\hat i + 3\hat j + \hat k$ and $\hat i + 2\hat j - 4\hat k$ is ....... $^o$

Answer

b
(b) $\cos \theta = \frac{{\vec A.\vec B}}{{|\vec A||\vec B|}} = \frac{{ - 2 + 6 - 4}}{{\sqrt {14} \sqrt {21} }} = 0$ 

$\therefore \theta = 90^\circ $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

An object is projected from ground with speed $20 \,m / s$ at angle $30^{\circ}$ with horizontal. Its centripetal acceleration one second after the projection is .......... $m / s ^2$ [Take $g=10 \,m / s ^2$ ]
A stream of a positively charged particles having $\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }$ and velocity $\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s$ is deflected by an electric field $1.8 \hat{ j } kV / m$. The electric field exists in a region of $10 cm$ along $x$ direction. Due to the electric field, the deflection of the charge particles in the $y$ direction is $...........mm$
A uniform magnetic field of $0.3\; T$ is established along the positive $Z$ -direction. A rectangular loop in $XY$ plane of sides $10 \;cm$ and $5 \;cm$ carries a current of $I =12\; A$ as shown. The torque on the loop is
Two long parallel conductors $S_{1}$ and $S_{2}$ are separated by a distance $10 \,cm$ and carrying currents of $4\, A$ and $2 \,A$ respectively. The conductors are placed along $x$-axis in $X - Y$ plane. There is a point $P$ located between the conductors (as shown in figure).

A charge particle of $3 \pi$ coulomb is passing through the point $P$ with velocity

$\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s$; where $\hat{i}$ and $\hat{j} \quad$ represents unit vector along $x$ and $y$ axis respectively.

The force acting on the charge particle is $4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N$. The value of $x$ is

In the following circuit, $5$ $\Omega$ resistor develops $45$ $J/s$ due to current flowing through it. The power developed per second across $12$ $\Omega$ resistor is ............. $W$
$\hat i.\left( {\hat j \times \,\,\hat k} \right) + \;\,\hat j\,.\,\left( {\hat k \times \hat i} \right) + \hat k.\left( {\hat i \times \hat j} \right)=$
Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed $10 ms^{-1}$. If the minimum time interval between two instants when the string is flat is $0.5\, s$, the wavelength of the waves is .... $m$
Magnetic flux in a circuit containing a coil of resistance $2\,\Omega $ changes from $2.0 \,Wb$ to $10 \,Wb$ in $0.2 \,sec$. The charge passed through the coil in this time is......$C$
A step-up transformer operates on a $230\, V$ line and supplies a load of $2$ $ampere$. The ratio of the primary and secondary windings is $1 : 25$. The current in the primary is....$A$
The diode shown in the circuit is a silicon diode. The potential difference between the points $A$ and $B$ will be.....$V$