Vector Algebra | Mathematics | WB JEE Previous Year Questions

Vector Algebra

MCQ (Single Correct Answer)

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}, \lambda \vec{b}+4 \vec{c}$ and $(2 \lambda-1) \vec{c}$ are non-coplanar for

WB JEE 2025

If ' $\theta$ ' is the angle between two vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}|=7,|\vec{b}|=1$ and $|\vec{a} \times \vec{b}|^2=k^2-(\vec{a} \cdot \vec{b})^2$, then the values of $k$ and $\theta$ are

WB JEE 2025

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be vectors of equal magnitude such that the angle between $\vec{a}$ and $\vec{b}$ is $\alpha, \vec{b}$ and $\vec{c}$ is $\beta$ and $\vec{c}$ and $\vec{a}$ is $\gamma$. Then the minimum value of $\cos \alpha+\cos \beta+\cos \gamma$ is

WB JEE 2025

If $\vec{\alpha}=3 \vec{i}-\vec{k},|\vec{\beta}|=\sqrt{5}$ and $\vec{\alpha} \cdot \vec{\beta}=3$, then the area of the parallelogram for which $\vec{\alpha}$ and $\vec{\beta}$ are adjacent sides is

WB JEE 2025

Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors. Suppose $\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0$ and the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{6}$. Then $\vec{a}$ is

WB JEE 2025

A unit vector in XY-plane making an angle $$45^{\circ}$$ with $$\hat{i}+\hat{j}$$ and an angle $$60^{\circ}$$ with $$3 \hat{i}-4 \hat{j}$$ is

WB JEE 2024

The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\widehat j + \widehat k,\overrightarrow \beta = \widehat j + a\widehat k$$ and $$\overrightarrow \gamma = a\widehat i + \widehat k$$ is maximum, is

WB JEE 2023

If the volume of the parallelopiped with $$\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overrightarrow c $$ and $$\overrightarrow c \times \overrightarrow a $$ as conterminous edges is 9 cu. units, then the volume of the parallelopiped with $$(\overrightarrow a \times \overrightarrow b ) \times (\overrightarrow b \times \overrightarrow c ),(\overrightarrow b \times \overrightarrow c ) \times (\overrightarrow c \times \overrightarrow a )$$, and $$(\overrightarrow c \times \overrightarrow a ) \times (\overrightarrow a \times \overrightarrow b )$$ as conterminous edges is

WB JEE 2023

If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c $$ is unit vector perpendicular to $$\overrightarrow a $$ and coplanar with $$\overrightarrow a $$ and $$\overrightarrow b $$, then unit vector $$\overrightarrow d $$ perpendicular to both $$\overrightarrow a $$ and $$\overrightarrow c $$ is

WB JEE 2022

If $${\overrightarrow \alpha }$$ is a unit vector, $$\overrightarrow \beta = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow \gamma = \widehat i + \widehat k$$ then the maximum value of $$\left[ {\overrightarrow \alpha \overrightarrow \beta \overrightarrow \gamma } \right]$$ is

WB JEE 2022

let $$\alpha$$, $$\beta$$, $$\gamma$$ be three non-zero vectors which are pairwise non-collinear. if $$\alpha$$ + 3$$\beta$$ is collinear with $$\gamma$$ and $$\beta$$ + 2$$\gamma$$ is collinear with $$\alpha$$ then $$\alpha$$ + 3$$\beta$$ + 6$$\gamma$$ is

WB JEE 2021

If a($$\alpha$$ $$\times$$ $$\beta$$) + b($$\beta$$ $$\times$$ $$\gamma$$) + c($$\gamma$$ + $$\alpha$$) = 0, where a, b, c are non-zero scalars, then the vectors $$\alpha$$, $$\beta$$, $$\gamma$$ are

WB JEE 2021

The unit vector in ZOX plane, making angles $$45^\circ $$ and $$60^\circ $$ respectively with $$\alpha = 2\widehat i + 2\widehat j - \widehat k$$ and $$\beta = \widehat j - \widehat k$$ is

WB JEE 2020

Let $$\widehat \alpha $$, $$\widehat \beta $$, $$\widehat \gamma $$ be three unit vectors such that $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )$$ where $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = $$$$(\widehat \alpha \,.\,\widehat \gamma )\widehat \beta - (\widehat \alpha \,.\,\widehat \beta )\widehat \gamma $$. If $$\widehat \beta $$ is not parallel to $$\widehat \gamma $$, then the angle between $$\widehat \alpha $$ and $$\widehat \beta $$ is

WB JEE 2019

The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\widehat j + 2\widehat k$$, $$5\widehat i - \widehat j + 2\widehat k$$ and $$4\widehat i - \widehat j - \lambda \widehat k$$, respectively. If the points A, B, C and D lie on a plane, the value of $$\lambda$$ is

WB JEE 2019

Let $$\overrightarrow \alpha $$ = $$\widehat i + \widehat j + \widehat k$$, $$\overrightarrow \beta $$ = $$\widehat i - \widehat j - \widehat k$$ and $${\overrightarrow \gamma }$$ = $$ - \widehat i - \widehat j - \widehat k$$ be three vectors. A vector $$\overrightarrow \delta $$, in the plane of $$\overrightarrow \alpha $$ and $$\overrightarrow \beta $$, whose projection on $${\overrightarrow \gamma }$$ is $${1 \over {\sqrt 3 }}$$, is given by

WB JEE 2018

Let $$\overrightarrow \alpha $$, $${\overrightarrow \beta }$$, $${\overrightarrow \gamma }$$ be the three unit vectors such that $$\overrightarrow \alpha .\overrightarrow \beta = \overrightarrow \alpha .\overrightarrow \gamma = 0$$ and the angle between $$\overrightarrow \beta $$ and $$\overrightarrow \gamma $$ is 30$$^\circ$$. Then $$\overrightarrow \alpha $$ is

WB JEE 2018

For any vector x, where $$\widehat i$$, $$\widehat j$$, $$\widehat k$$ have their usual meanings the value of $${(x \times \widehat i)^2} + {(x \times \widehat j)^2} + {(x \times \widehat k)^2}$$ where $$\widehat i$$, $$\widehat j$$, $$\widehat k$$ have their usual meanings, is equal to

WB JEE 2017

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

WB JEE 2017