# Vector Algebra · Physics · JEE Main

Start Practice## Numerical

JEE Main 2024 (Online) 9th April Evening Shift

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 betw...

JEE Main 2024 (Online) 9th April Morning Shift

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...

JEE Main 2024 (Online) 8th April Morning Shift

Three vectors $$\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$$ and $$\overrightarrow{\mathrm{OR}}$$ each of magnitude $$\mathrm{A}$$ are...

JEE Main 2024 (Online) 6th April Morning Shift

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 $$\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})$$,...

JEE Main 2024 (Online) 30th January Evening Shift

A vector has magnitude same as that of $$\vec{A}=3 \hat{i}+4 \hat{j}$$ and is parallel to $$\vec{B}=4 \hat{i}+3 \hat{j}$$. The $$x$$ and $$y$$ compone...

JEE Main 2023 (Online) 25th January Morning Shift

If $$\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k$$ and $$\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k...

JEE Main 2023 (Online) 24th January Morning Shift

Vectors $$a\widehat i + b\widehat j + \widehat k$$ and $$2\widehat i - 3\widehat j + 4\widehat k$$ are perpendicular to each other when $$3a + 2b = 7$...

JEE Main 2022 (Online) 28th July Morning Shift

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 ________...

JEE Main 2022 (Online) 26th July Evening Shift

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 ve...

JEE Main 2021 (Online) 22th July Evening Shift

Three particles P, Q and R are moving along the vectors $$\overrightarrow A = \widehat i + \widehat j$$, $$\overrightarrow B = \widehat j + \widehat...

JEE Main 2021 (Online) 25th February Evening Shift

If $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P $$, the angle between $$\overrightarrow P $$ and $$\ov...

JEE Main 2020 (Online) 7th January Evening Slot

The sum of two forces $$\overrightarrow P $$
and $$\overrightarrow Q $$
is $$\overrightarrow R $$
such that $$\left| {\overrightarrow R } \right| =...

## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 5th April Morning Shift

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

JEE Main 2024 (Online) 31st January Evening Shift

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

JEE Main 2023 (Online) 15th April Morning Shift

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

JEE Main 2023 (Online) 11th April Evening Shift

When vector $$\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}$$ is subtracted from vector $$\overrightarrow{\mathrm{B}}$$, it gives a vector
equal to $$2 \hat{...

JEE Main 2023 (Online) 8th April Morning Shift

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

JEE Main 2023 (Online) 24th January Evening Shift

If two vectors $$\overrightarrow P = \widehat i + 2m\widehat j + m\widehat k$$ and $$\overrightarrow Q = 4\widehat i - 2\widehat j + m\widehat k$$ a...

JEE Main 2022 (Online) 29th June Morning Shift

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. If magnitude of $$\overrightarrow A $$ + $$\overrightarrow B $$ i...

JEE Main 2022 (Online) 25th June Morning Shift

$$\overrightarrow A $$ is a vector quantity such that $$|\overrightarrow A |$$ = non-zero constant. Which of the following expression is true for $$\o...

JEE Main 2022 (Online) 25th June Morning Shift

Which of the following relations is true for two unit vector $$\widehat A$$ and $$\widehat B$$ making an angle $$\theta$$ to each other?

JEE Main 2021 (Online) 31st August Evening Shift

Statement I :Two forces $$\left( {\overrightarrow P + \overrightarrow Q } \right)$$ and $$\left( {\overrightarrow P - \overrightarrow Q } \right)$$ ...

JEE Main 2021 (Online) 27th August Morning Shift

The resultant of these forces $$\overrightarrow {OP} ,\overrightarrow {OQ} ,\overrightarrow {OR} ,\overrightarrow {OS} $$ and $$\overrightarrow {OT} $...

JEE Main 2021 (Online) 26th August Evening Shift

The angle between vector $$\left( {\overrightarrow A } \right)$$ and $$\left( {\overrightarrow A - \overrightarrow B } \right)$$ is :...

JEE Main 2021 (Online) 26th August Morning Shift

The magnitude of vectors $$\overrightarrow {OA} $$, $$\overrightarrow {OB} $$ and $$\overrightarrow {OC} $$ in the given figure are equal. The directi...

JEE Main 2021 (Online) 27th July Morning Shift

Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O' such that $$\left| {\overrightarrow {AB} } \right| = \left| {\ov...

JEE Main 2021 (Online) 25th July Evening Shift

Two vectors $$\overrightarrow X $$ and $$\overrightarrow Y $$ have equal magnitude. The magnitude of ($$\overrightarrow X $$ $$-$$ $$\overrightarrow Y...

JEE Main 2021 (Online) 25th July Morning Shift

Match List - I with List - IIChoose the correct answer from the options given below :...

JEE Main 2021 (Online) 22th July Evening Shift

What will be the projection of vector $$\overrightarrow A = \widehat i + \widehat j + \widehat k$$ on vector $$\overrightarrow B = \widehat i + \wid...

JEE Main 2021 (Online) 20th July Evening Shift

Two vectors $${\overrightarrow P }$$ and $${\overrightarrow Q }$$ have equal magnitudes. If the magnitude of $${\overrightarrow P + \overrightarrow Q...

JEE Main 2021 (Online) 20th July Morning Shift

If $$\overrightarrow A $$ and $$\overrightarrow B $$ are two vectors satisfying the relation $$\overrightarrow A $$ . $$\overrightarrow B $$ = $$\left...

JEE Main 2021 (Online) 25th February Morning Shift

In an octagon ABCDEFGH of equal side, what is the sum of $$\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE...

JEE Main 2019 (Online) 8th April Evening Slot

Let $$\left| {\mathop {{A_1}}\limits^ \to } \right| = 3$$, $$\left| {\mathop {{A_2}}\limits^ \to } \right| = 5$$ and $$\left| {\mathop {{A_1}}\limi...

JEE Main 2019 (Online) 10th January Evening Slot

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. The magnitude of $$\left( {\overrightarrow A + \overrightarrow ...

JEE Main 2019 (Online) 10th January Morning Slot

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 -
...

JEE Main 2018 (Online) 16th April Morning Slot

Let $$\overrightarrow A $$ = $$\left( {\widehat i + \widehat j} \right)$$ and, $$\overrightarrow B = \left( {2\widehat i - \widehat j} \right).$$ The...

AIEEE 2004

If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$, then the angle beetween A and B is