If A =(2 i +3 j - k ) ;m and B =( i +2 j +2 k ) ; m. The magnitud… - Vidyadip

MCQ

If $\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m$ and $\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m$. The magnitude of component of vector $\overrightarrow{ A }$ along vector $\vec{B}$ will be $......m$.

✓
$2$
B
$1$
C
$3$
D
$4$

✓

Answer

Correct option: A.

$2$

a
$\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) m \text { and } \overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k }) m$

Component of $\overrightarrow{ A }$ along $\overrightarrow{ B }=\overrightarrow{ A } \cdot \hat{ B }$

$=\frac{\overrightarrow{ A } \overrightarrow{ B }}{|\overrightarrow{ B }|}$ $=\frac{2+6-2}{\sqrt{1^{2}+2^{2}+2^{2}}}$

$=\frac{6}{3}=2$

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

Explore more

More "M.C.Q (1 Marks)" from 3.1 vectors→3.1 vectors — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A spherical rigid ball is released from rest and starts rolling down an inclined plane from height $h=7 \,m$, as shown in the figure. It hits a block at rest on the horizontal plane (assume elastic collision). If the mass of both the ball and the block is $m$ and the ball is rolling without sliding, then the speed of the block after collision is close to ............. $m/s$

A ball falls from a height of $5\,m$ and strikes the roof of a lift. If at the time of collision, lift is moving in the upward direction with a velocity of $1\,m/s$, then the velocity with which the ball rebounds after collision will be $-(e = 1)$

A bomb of mass $12\,\,kg$ at rest explodes into two fragments of masses in the ratio $1 : 3.$ The $K.E.$ of the smaller fragment is $216\,\,J.$ The momentulm of heavier fragment is (in $kg-m/sec$ )

What is the number of significant figures in $ 0.310\times 10^3$

A source is moving towards an observer with a speed of $20 m/s$ and having frequency of $240 Hz.$ The observer is now moving towards the source with a speed of $20 m/s$. Apparent frequency heard by observer, if velocity of sound is $340 m/s$, is ... $Hz$

A satellite moves around the earth in a circular orbit of radius $r$ with speed $v$. If the mass of the satellite is $M$, its total energy is

Two blocks of mass $2 \,kg$ and $4 kg$ are accelerated with same acceleration by a force $10 \,N$ as shown in figure on a smooth horizontal surface. Then the spring force between the two blocks will be .......... $N$ (spring is massless)

Which one of the following statements is incorrect?

A point mass $m$ is placed outside a hollow spherical shell of mass $M$ and uniform density at a distanced from centre of the big sphere.Gravitational force on point mass mat $P$ is:

A sample of gas expands from $V_1$ to $V _2$. In which of the following, the work done will be greatest ?