The component of vector A=2 i+3 j along the vector i+j is - Vidyadip

MCQ

The component of vector $A=2 \hat{i}+3 \hat{j}$ along the vector $\hat{i}+\hat{j}$ is

✓
$\frac{5}{\sqrt{2}}$
B
$10 \sqrt{2}$
C
$5 \sqrt{2}$
D
5

✓

Answer

Correct option: A.

$\frac{5}{\sqrt{2}}$

(a) $\frac{\vec{A} \cdot \vec{B}}{|\vec{i}+\vec{j}|}=\frac{(2 \hat{i}+3 \hat{j})(\hat{i}+\hat{j})}{\sqrt{2}}=\frac{2+3}{\sqrt{2}}=\frac{5}{\sqrt{2}}$

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 "MCQ" from Vector→Vector — all question types→JEE physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

A string on a musical instrument is $50 \mathrm{~cm}$ long and its fundamental frequency is $270 \mathrm{~Hz}$. If the desired frequency of $1000 \mathrm{~Hz}$ is to be produced, the required length of the string is

Two satellite $A$ and $B$, ratio of masses $3: 1$ are in circular orbits of radii $r$ and $4 r$. Then ratio of total mechanical energy of $A$ to $B$ is

A thin convex lens of refractive index $1.5$ has a focal length of $15 \mathrm{~cm}$ in air. When the lens is placed in liquid of refractive index $4 / 3$, its focal length will be

A cold soft drink is kept on the balance. When the cap is open, then the weight

The magnetic induction in the region between the pole faces of an electromagnet is $0.7$ weber $/ \mathrm{m}$. The induced e.m.f. in a straight conductor $10 \mathrm{~cm}$ long, perpendicular to $B$ and moving perpendicular both to magnetic induction and its own length with a velocity $2\ \mathrm{m} / \mathrm{sec}$ is

The temperature of the sun is measured with

A simple pendulum is hanging from a peg inserted in a vertical wall. lts bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is $\frac{2}{\sqrt{5}}$. After how many collisions the amplitude of vibration will become less than $60^{\circ}$

A particle free to move along the $x$-axis has potential energy given by $U(x)=k\left[1-\exp (-x)^2\right]$ for $-\infty \leq x \leq+\infty$, where $k$ is a positive constant of appropriate dimensions. Then

A balloon is rising vertically up with a velocity of $29 ms$. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it is $(g=9.8 ms )$

In a hydrogen atom, which of the following electronic transitions would involve the maximum energy change