List of top Mathematics Questions on Vectors

If $|\vec a |=1 $, $|\vec b|=4$, $\vec a \times \vec b = 2$. If $\vec c= ( \vec a \times \vec b)-3 \vec b$ Then the angle between $\vec b$ and $\vec c$ is

Let a =$\^i+4\^j+2\^k,b=3\^i−2\^j+7\^k \,\,\,\,and\,\,\.\ c=2\^i−\^j+4\^k$. Find a vector d satisfies $\overrightarrow{d}\times{\overrightarrow{b}}=\overrightarrow{c}\times{\overrightarrow{b}}$ and $\overrightarrow{d}.\overrightarrow{a}=24$, then $|\overrightarrow{d}|^2$ is equal to

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non zero vectors such that $\vec{b} \cdot \vec{c}=0$ and $\vec{a} \times(\vec{b} \times \vec{c})=\frac{\vec{b}-\vec{c}}{2}$ If $\vec{d}$ be a vector such that $\vec{b} \cdot \vec{d}=\vec{a} \cdot \vec{b}$, then $(\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d})$ is equal to

Let $\Delta, \nabla \in\{\Lambda, V\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

Let l₁ and l₂be the lines r₁ = λ($\hat{i}+\hat{j}+\hat{k}$) and r₂ = ($\hat{j}-\hat{k}$) + μ ($\hat{i}+\hat{k}$), respectively. Let X be the set of all the planes H containing line l₁. For a plane H, let d (H) denote the smallest possible distance between the points of l₂ and H. Let H₀ be a plane in X for which d (H₀) is the maximum value of d (H ) as H varies over all planes in X . Match each entry in List-I to the correct entries in List-II.

List-I		List-II
(P)	The value of d (H₀) is	(1)	$\sqrt3$
(Q)	The distance of the point (0,1,2) from H₀ is	(2)	$\frac{1}{\sqrt3}$
(R)	The distance of origin from H₀ is	(3)	0
(S)	The distance of origin from the point of intersection of planes y = z, x = 1, and H₀ is	(4)	$\sqrt2$
		(5)	$\frac{1}{\sqrt2}$

The correct option is:

Let a b, and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be $a-b+c$, $λa-3b+4c$, $-a+2b-3c$ and $2a-4b+6c$ respectively. If AB AC , and AD are coplanar, then λ is equal to ____.

Let $\overrightarrow{a}=3\^i+\^j −\^k$ and $\overrightarrow{c}=2\^i+3\^j −3\^k$ if $\overrightarrow{b}$ is a vector such that $\overrightarrow{a}=\overrightarrow{b}\times\overrightarrow{c}$ and $|\overrightarrow{b}|=50$ , then $|72|\overrightarrow{b}+\overrightarrow{c}|^2|$| | is equal to _______.

Let a, b, c be three distinct real numbers, none equal to one. If the vectors $a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c\hat{k}$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is equal to

Let $\overrightarrow{a}=2\^i+7\^j−\^k ,\overrightarrow{b} =3\^i+5 \^k$ and $\overrightarrow{c}=\^i=\^j+2\^k$ . Let $\overrightarrow{d}$ be a vector which is perpendicular to both $\overrightarrow{a}$ and $\overrightarrow{b}$ , and $\overrightarrow{c}.\overrightarrow{d}=12$. Then $(-\^i+\^j=\^k).(\overrightarrow{c}\times\overrightarrow{d})$ is equal to

Let $λ∈Z ,→a=λ\^i+\^j =/^ k λ ∈$ and $\overrightarrow{ b} = 3 \^i− \^j + 2 \^k$ . be a vector such that ( $\overrightarrow{ a}+\overrightarrow{ b}+\overrightarrow{ c}$ ) × $\overrightarrow{ c}=\overrightarrow{ 0},\overrightarrow{ a}.\overrightarrow{ c}$ and $\overrightarrow{ b}.\overrightarrow{ C}=-20$ Then $ | \overrightarrow{c} + ( λ \^i + \^j + \^k ) | ^2 $ is equal to

Let a, b, c be three distinct real numbers, none equal to one. If the vectors $a\^i+\^j+\^k , \^i+b\^j+\^k$ and $ \^i+\^j+c\^k $ are coplanar, then $\frac{1}{ 1 − a }+ \frac{1}{ 1 − b} + \frac{1 }{1 − c }$ is equal to

$5\^{i}+5\hat{j}+2λ\hat{k},\hat{i}+2\hat{j}+3\hat{k},-2\hat{i}+λ\hat{j}+4\hat{k}$ and $-\hat{i}+5\hat{j}+6\hat{k}.$ Let the set S = {λ∈ $\mathbb{R}$ : The points A, B, C and D are coplanar}. Then $\displaystyle\sum_{λ∈S}^{}(λ+2)^2$ is equal to

Let the vectors $\overrightarrow{ a} , \overrightarrow{ b}, \overrightarrow{ c} $represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by $\overrightarrow{ a} , \overrightarrow{ b}, \overrightarrow{ c} $ and $\overrightarrow{ a} ,2 \overrightarrow{ b},3 \overrightarrow{ c} $ is equal to

The component of $\hat{i}$ in the direction of the vector $\hat{i}+\hat{j}+2\hat{k}$ is

If value of the cross product (ax5(→)is_______

Given below are two statements:
Statement I: Three points with position vectors $\vec{a},\vec{b},\vec{c}$ are collinear if there exists scalars x,y,z not all zero such that $x\vec{a} + y\vec{b} + z\vec{c} = 0$, where x+y+z=0.
Statement II: Scalar product and vector product are both commutative.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Which of the following is not correct?
(A) Sum of the vectors directed from the vertices to the mid-points of opposite side of a triangle is zero.
(B) Medians of a triangle are not concurrent.
(C) The diagonals of a quadrilateral bisect each other iff it is a parallelogram.
(D) Vectors having the different terminal point are called co-terminus vectors.
Choose the correct answer from the options given below:

Given below are two statements:
Statement I: Let $\vec{a}$, $\vec{b}$, $\vec{c}$ be three vectors. Then the scalar $(\vec{a}\times\vec{b})·\vec{c}$ is called the scalar product of $\vec{a},\vec{b},\vec{c}$ and is denoted by $[\vec{a}\vec{b}\vec{c}]=\vec{a}·(\vec{b}\times\vec{c})$.
Statement II: $\vec{a}\times\vec{b}$ is vector which is ⊥ to $\vec{a}$ and $\vec{b}$ both.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Given below are two statements:
Statement I: The vector equation of line passing through two points with position vector $\vec{a}$ and $\vec{b}$ is $\vec{r} = \vec{a} +\lambda(\vec{b}+\vec{a})$
Statement II: The vector equation of a straight line passing through a fixed point with position vector $\vec{a}$ and parallel to a given vector $\vec{b}$ is $\vec{r}=\vec{a}+λ\vec{b}$ where λ is scalar.
In the light of the above Statements, choose the most appropriate answer from the options given below :

if $\vec{a}$, $\vec{b}$ and $\vec{c}$ are three non-coplanar vectors, then $(\vec{a}+\vec{b}+\vec{c}) [(\vec{a}+\vec{b})\times(\vec{a}+\vec{c})]$ equal to

If $\vec{a},\vec{b},\vec{c}$ are non-coplanar unit vectors such that $\vec{a}\times(\vec{b}\times \vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt2}$ then the angle between a and b is

Three vectors a, b and c are given. Find the equation of a vector that lies in the plane of vector a and vector b and whose projection on vector c is 1/√3.

Match List-I and List-II

LIST I		LIST II
A.	$\|\vec{A}+\vec{B}\|=\|\vec{A}-\vec{B}\|$	I.	45°
B.	$\|\vec{A}\times\vec{B}\|=\vec{A}.\vec{B}$	II.	30°
C.	$\|\vec{A}.\vec{B}\|=\frac{AB}{2}$	III.	90°
D.	$\|\vec{A}\times\vec{B}\|=\frac{AB}{2}$	IV.	60°

Choose the correct answer from the options given below:

If $\vec{a}=2\vec{i}+2\vec{j}+3\vec{k},\vec{b}=\vec{i}+2\vec{j}+\vec{k}\;and\;\vec{c}=3\vec{i}+\vec{j}$ are such that $\vec{a}+\gamma\vec{b}$ is perpendicular to $\vec{c}$ then determine the value of $\gamma$?

LIST I		LIST II
A.	\(\|\vec{A}+\vec{B}\|=\|\vec{A}-\vec{B}\|\)	I.	45°
B.	\(\|\vec{A}\times\vec{B}\|=\vec{A}.\vec{B}\)	II.	30°
C.	\(\|\vec{A}.\vec{B}\|=\frac{AB}{2}\)	III.	90°
D.	\(\|\vec{A}\times\vec{B}\|=\frac{AB}{2}\)	IV.	60°

List of top Mathematics Questions on Vectors

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