Question
The angle between $\vec{\text{A}}=\hat{\text{i}}+\hat{\text{j}}$ and $\vec{\text{B}}=\hat{\text{i}}-\hat{\text{j}}$ is
- 45°
- 90°
- –45°
- 180°
✓
Answer
- 90°
Explanation:
Given
$\vec{\text{A}}=\hat{\text{i}}+\hat{\text{j}}$$\vec{\text{B}}=\hat{\text{i}}-\hat{\text{j}}$
$\vec{\text{A}}.\vec{\text{B}}=|\text{A}||\text{B}|\cos\theta$
$\cos\theta=\frac{\vec{\text{A}}.\vec{\text{B}}}{|\text{A}||\text{B}|}$
$=\frac{(\hat{\text{i}}+\hat{\text{j}}).(\hat{\text{i}}-\hat{\text{j}})}{\sqrt{1^2+1^2}\times\sqrt{1^2+(-1)^2}}=\frac{1-1}{2}=0$
$\Rightarrow\cos\theta=\cos90$
$\therefore\theta=90^\circ.$ Hence, verifies the option (b).
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
In the arrangement shown, the $2\, kg$ block is held to keep the system at rest. The string and pulley are ideal. When the $2\, kg$ block is set free, by what amount the tension in the string changes? $[ g = 10\, m/s^2]$
→A man standing on a cliff claps his hand hears its echo after $1 \,sec$. If sound is reflected from another mountain and velocity of sound in air is $340\, m/sec.$ Then the distance between the man and reflection point is ..... $m$
→Two satellites $A$ and $B$ of masses $200\, kg$ and $400\, kg$ are revolving round the earth at height of $600\, km$ and $1600\, km$ respectively. If $T _{ A }$ and $T _{ B }$ are the time periods of $A$ and $B$ respectively then the value of $T _{ B }- T _{ A }$
→[Given : radius of earth $=6400\, km$, mass of earth $=6 \times 10^{24}\, kg$ ]
Average density of the earth:
$A$ uniform rod of mass $m$ and length $l$ hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinge when the rod becomes vertical is :
→During illness an $80\, kg$ man ran a fever of $102.2^o F$ instead of normal body temperature of $98.6^o F$. Assuming that human body is mostly water, how much heat is required to raise his temperature by that amount .......... $kcal$
→$Assertion :$ In simple harmonic motion, the motion is to and fro and periodic
$Reason :$ Velocity of the particle $(v) = \omega \sqrt {k^2 - x^2}$ (where $x$ is the displacement).
→$Reason :$ Velocity of the particle $(v) = \omega \sqrt {k^2 - x^2}$ (where $x$ is the displacement).
The ratio of mean kinetic energy of hydrogen and nitrogen at temperature $300 \,K$ and $450\, K$ respectively is
→If vectors $\overrightarrow {A} = cos\omega t\hat i + sin\omega t\hat j$ and $\overrightarrow {B} = cos\frac{{\omega t}}{2}\hat i + sin\frac{{\omega t}}{2}\hat j$ are functions of time, then the value of $t$ at which they are orthogonal to each other is
→The coefficient of restitution $e$ for a perfectly elastic collision is
→