Q JEE Main 2024

If $\vec{a}$ and $\vec{b}$ 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...

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Q JEE Main 2019

In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD...

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Q JEE MAIN 2021

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Q JEE MAIN 2021

Statement :1 If three forces $\vec{F}_1, \vec{F}_2$ and $\vec{F}_3$ are represented by three sides of a triangle and $\vec{F}_1+\vec{F}_2=-\vec{F}_3$, then...

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Q JEE MAIN 2021`

Statement I: Two forces $\left(\stackrel{\Delta \stackrel{\Delta}{\mathrm{P}}+\stackrel{\Delta}{\mathrm{Q}})}{(\stackrel{\Delta}{\mathrm{P}}-\stackrel{\Delta}{\mathrm{Q}})}\right.$ and where $^{(\stackrel{\Delta}{\mathrm{P}} \perp \stackrel{\Delta}{\mathrm{Q}})}$, when act at an angle $\theta_1$ to each other,...

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Q JEE-MAIN 2021

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

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Q JEE MAIN 2021

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

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Q JEE MAIN 2021

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...

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Q JEE MAIN 2021

Three particles P, Q and R are moving along the vectors $\vec{A}=\hat{i}+\hat{j}, \vec{B}=\hat{j}+\hat{k}$ and $\vec{C}=-\hat{i}+\hat{j}$ respectively. They strike on a...

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Q JEE-MAIN 2021

Match List I with List II

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Q JEE MAIN 2021

Assertion $\mid \mathrm{A}$ : If $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are four points on a semi-circular arc with centre at '...

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Q JEE MAIN 2021

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

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Q JEE MAIN 2019

Let $\left|\overrightarrow{A_1}\right|=3,\left|\overrightarrow{A_2}\right|=5$ and $\left|\overrightarrow{A_1}+\overrightarrow{A_2}\right|=5$. The value of $\left(2 \overrightarrow{A_1}+3 \overrightarrow{A_2}\right) \cdot\left(3 \overrightarrow{A_1}-2 \overrightarrow{A_2}\right)$ is:

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Q JEE MAIN 2021

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 $|\vec{A}-\vec{B}|$...

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Q JEE MAIN 2021

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

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Q JEE MAIN 2021

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Q JEE MAIN 2021

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, $\overrightarrow{A O}=2 \hat{i}+3 \hat{j}-4 \hat{k}$

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Q JEE MAIN 2022

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

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Q JEE Main 2022

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...

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Q JEE-MAIN 2022

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. If-magnitude of $\vec{A}+\vec{B}$ is equal to two times the magnitude of $\vec{A}-\vec{B}$,...

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Q JEE MAIN_2023

If force $\vec{F}=3 \hat{i}+4 \hat{j}-2 \hat{k}$ acts on a particle having position vector $2 \hat{i}+\hat{j}+2 \hat{k}$ then, the torque about...

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Q JEE MAIN 2022

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

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Q JEE MAIN 2022

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

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Q JEE MAIN 20241

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

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Q JEE MAIN 2024

A vector has magnitude same as that of $\overrightarrow{\mathrm{A}}-=3 \hat{\jmath}+4 \hat{\jmath}$ and is parallel to $\overrightarrow{\mathrm{B}}=4 \hat{\imath}+3 \hat{\jmath}$. The $x$...

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Q JEE MAIN 2023

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 $3 a+2 b=7$, the ratio...

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Q JEE MAIN_2023

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

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Q JEE MAIN 2023

Which of the following metals can be extracted through alkali leaching technique?

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Q JEE MAIN 2023

A vector in $x$ - $y$ plane makes an angle of $30^{\circ}$ with $y$-axis. The magnitude of $y$-component of vector...

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Q JEE MAIN 2023

The reaction representing the Mond process for metal refining is ______ [

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Q JEE MAIN 2023

If and then, The unit vector in the direction of is . The value of x is

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Q JEE MAIN 2024

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...

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Q JEE MAIN

For three vectors $\vec{A}=(-x \hat{\imath}-6 \hat{\jmath}-2 \hat{k}), \vec{B}=(-\hat{\imath}+4 \hat{\jmath}+3 \hat{k})$ and $\vec{C}=(-8 \hat{\imath}-\hat{\jmath}+3 \hat{k})$, if $\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0$, them...

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