Vector — JEE Main PYQs

When the position vector $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$ changes sign as $-\overrightarrow{\mathrm{r}}$, which one of the following vector will not flip under sign change ?

Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A}=2\hat{i}+3n\hat{j}+2\hat{k}$ and $\overrightarrow{\mathrm{B}}=2\hat{\mathrm{i}}-2\hat{\mathrm{j}}+4\mathrm{p}\hat{\mathrm{k}}$, respectively. If both the vec …

Two forces ${\overrightarrow{\mathrm{F}}}_1$ and ${\overrightarrow{\mathrm{F}}}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between …

A particle moves in $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\overrightarrow{\mathrm{P}}(\mathrm{t})=\hat{\mathrm{i}}\cos (\mathrm{kt})-\hat{\mathrm{j}}\sin (\mathrm{kt})$. If k is constant, the angle between …

The angle between vector $\overrightarrow{\mathrm{Q}}$ and the resultant of $(2\overrightarrow{\mathrm{Q}}+2\overrightarrow{\mathrm{P}})$ and $(2\overrightarrow{\mathrm{Q}}-2\overrightarrow{\mathrm{P}})$ is:

For three vectors $\vec{A}=(-x\hat{i}-6\hat{j}-2\hat{k})$, $\vec{B}=(-\hat{i}+4\hat{j}+3\hat{k})$ and $\vec{C}=(-8\hat{i}-\hat{j}+3\hat{k})$, if $\vec{A}\cdot (\vec{B}\times \vec{C})=0$, then value of x is ______.

Three vectors $\overrightarrow{\mathrm{OP}}$, $\overrightarrow{\mathrm{OQ}}$ and $\overrightarrow{\mathrm{OR}}$ each of magnitude A are acting as shown in figure. The resultant of the three vectors is $\mathrm{A}\sqrt{\mathrm{x}}$. The value of x is ____.

If $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ makes an angle ${\cos }^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ The integer value of n is ____.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is

A vector has magnitude same as that of $\overrightarrow{\mathrm{A}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and is parallel to $\overrightarrow{\mathrm{B}}=4\hat{\mathrm{i}}+3\hat{\mathrm{j}}$. The x and y components of this vector in first quadrant are x and 3 respectively where …

If two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ having equal magnitude R are inclined at an angle $\theta$, then

Two forces having magnitude A and $\frac{\mathrm{A}}{2}$ are perpendicular to each other. The magnitude of their resultant is

A vector in $\mathrm{x}-\mathrm{y}$ plane makes an angle of $30^{\circ }$ with y-axis. The magnitude of y-component of vector is $2\sqrt{3}$. The magnitude of x-component of the vector will be :

Vectors $a\hat{i}+b\hat{j}+\hat{k}$ and $2\hat{i}-3\hat{j}+4\hat{k}$ are perpendicular to each other when $3a+2b=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is ______.

If two vectors $P=\hat{i}+2m\hat{j}+m\hat{k}$ and $\overrightarrow{\mathrm{Q}}=4\hat{\mathrm{i}}-2\hat{\mathrm{j}}+\mathrm{m}\hat{\mathrm{k}}$ are perpendicular to each other. Then, the value of m will be :

If $\vec{P}=3\hat{i}+\sqrt{3}\hat{j}+2\hat{k}$ and $\vec{Q}=4\hat{i}+\sqrt{3}\hat{j}+2.5\hat{k}$ then, The unit vector in the direction of $\vec{P}\times \vec{Q}$ is $\frac{1}{x}(\sqrt{3}\hat{i}+\hat{j}-2\sqrt{3}\hat{k})$. The value of $x$ is

If the projection of $2\hat{i}+4\hat{j}-2\hat{k}$ on $\hat{i}+2\hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be

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

Two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ have equal magnitudes. If magnitude of $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ is equal to two times the magnitude of $\vec{A}-\vec{B}$, then the angle between $\vec{A}$ and $\vec{B}$ wi …

$\overrightarrow{\mathrm{A}}$ is a vector quantity such that $|\overrightarrow{\mathrm{A}}|=$ nonzero constant. Which of the following expressions is true for $\overrightarrow{\mathrm{A}}$ ?

Which of the following relations is true for two unit vectors $\hat{\mathrm{A}}$ and $\hat{\mathrm{B}}$ making an angle $\theta$ to each other?

The magnitude of vectors $\overrightarrow{OA}$, $\overrightarrow{OB}$ and $\overrightarrow{OC}$ in the given figure are equal. The direction of $\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{OC}$ with $x$-axis will be :-

The angle between vector $(\vec{A})$ and $(\vec{A}-\vec{B})$ is:

If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A}\cdot \vec{B}=|\vec{A}\times \vec{B}|$. Then the value of $|\vec{A}-\vec{B}|$ will be:

Two vectors $\vec{P}$ and $\vec{Q}$ have equal magnitudes. If the magnitude of $\vec{P}+\vec{Q}$ is $n$ times the magnitude of $\vec{P}-\vec{Q}$, then angle between $\vec{P}$ and $\vec{Q}$ is :

In an octagon $ABCDEFGH$ of equal side, what is the sum of $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}+\overrightarrow{\mathrm{AG}}+\overrightarrow{\mathrm{AH}}$, if, …

What will be the projection of vector $\overrightarrow{\mathrm{A}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ on vector $\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ ?

Three particles $P,Q$ and $R$ are moving along the vectors $\vec{A}=\hat{i}+\hat{j},\vec{B}=\hat{j}+\hat{k}$ and $\overrightarrow{\mathrm{C}}=-\hat{\mathrm{i}}+\hat{\mathrm{j}}$ respectively. They strike on point and start to move in different directions. Now particle P …

The resultant of these forces $\overrightarrow{\mathrm{OP}},\overrightarrow{\mathrm{OQ}},\overrightarrow{\mathrm{OR}},\overrightarrow{\mathrm{OS}}$ and $\overrightarrow{\mathrm{OT}}$ is approximately ..... N [Take $\sqrt{3}=1.7,\sqrt{2}=1.4$. Given $\hat{i}$ and …

Statement-I: Two forces $(\vec{P}+\vec{Q})$ and $(\vec{P}-\vec{Q})$ where $\vec{P}\perp \vec{Q}$, when act at an angle ${\theta }_1$ to each other, the magnitude of their resultant is $\sqrt{3\left({\mathrm{P}}^2+{\mathrm{Q}}^2\right)}$, when they act at an angle …

Assertion A: If A, B, C, D are four points on a semicircular arc with centre at 'O' such that $|\overrightarrow{\mathrm{AB}}|=|\overrightarrow{\mathrm{BC}}|=|\overrightarrow{\mathrm{CD}}|$, then …

Match List I with List II.

List - I
(a) $\overrightarrow{C}-\overrightarrow{A}-\overrightarrow{B}=0$
(b) $\overrightarrow{A}-\overrightarrow{C}-\overrightarrow{B}=0$
(c) $\overrightarrow{B}-\overrightarrow{A}-\overrightarrow{C}=0$
(d) …

Two vectors $\vec{X}$ and $\vec{Y}$ have equal magnitude. The magnitude of $(\vec{X}-\vec{Y})$ is $n$ times the magnitude of $(\vec{X}+\vec{Y})$. The angle between $\vec{X}$ and $\vec{Y}$ is :

Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. A vertical force $\vec{P}$ of magnitude 100 N is applied at point A of the frame. Suppose the force is $\overrightarrow{\mathrm{P}}$ resolved parallel to the arms AB and AC of …

The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $|\vec{R}|=|\vec{P}|$. The angle $\theta$ (in degrees) that the resultant of $2\vec{P}$ and $\vec{Q}$ will make with $\vec{Q}$ is, ______.

Let $|{\vec{A}}_1|=3$, $|{\vec{A}}_2|=5$, and $|{\vec{A}}_1+{\vec{A}}_2|=5$. The value of $(2{\vec{A}}_1+3{\vec{A}}_2)\cdot (3{\vec{A}}_1-2{\vec{A}}_2)$ is:

In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:

If $\vec{A}\times \vec{B}=\vec{B}\times \vec{A}$, then the angle between $A$ and $B$ is