Three vectors satisfy the relation $\displaystyle \overrightarrow { A } .\overrightarrow { B } =0$ and $\displaystyle \overrightarrow { A } .\overrightarrow { C } =0$, then $\displaystyle \overrightarrow { A } $ is parallel to:

Vectors $\bar { A }$, $\bar { B }$ and $\bar { C }$ are such that $ \bar { A } \bullet \bar { B } =0$ and $ \bar { A } \bullet \bar { C } =0$. Then the vector parallel to $\bar { A }$ is

The vector $\overrightarrow { B } = 5\hat { i } + 2\hat {  j}-S \hat {  k} $ is perpendicular to the vector $\overrightarrow {  A}= 3\hat {  i} +\hat { j } + 2\hat {k  } $ if S=

$\vec {A}$ and $\vec {B}$ are vectors expressed as $\vec {A} =2\hat {i}+\hat {j}$ and $\vec {B} =\hat {i}-\hat {j}$. Unit vector perpendicular to $\vec {A}$ and $\vec {B}$ is

Two particles are simultaneously projected in opposite direction horizontally from a given point in space where gravity g is uniform.If $u _1 and u _2$ be their initial speeds, then the time t after which their velocities are mutually perpendicular is given by

If the magnitude of two vectors are $8$ unit and $5$ and their scalar product is zero, the angle between the two vectors is

If $\overrightarrow { A } +\overrightarrow { B } =\overrightarrow { R }$ and $\left( \overrightarrow { A } +2\overrightarrow { B }  \right)$ is perpendicular to $\overrightarrow { A }$, then

The angle between the vectors $(\overline{\mathrm{A}}$ x $\overline{\mathrm{B}})$ and $(\overline{\mathrm{B}}\times\overline{\mathrm{A}})$ is:

In a clockwise system, which of the following is true?

The value of $ (\bar { A } +\bar { B } )\times (\bar { A } -\bar { B } )$ is 

The velocity of a particle is $\vec{v}=6\hat{i}+2\hat{j}-2\hat{k}.$ The component of the velocity parallel to vector $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ is :- 

If $\overline {A} \times\overline {B} =\overline {C}$ which of the following statement is not correct?

Two forces of magnitude 20N and 20N act along the adjacent sides of the parallelogram and the magnitude of the resultant force of these two forces is $20\sqrt{3}$. Then the angle between these forces is:

What is the unit vector perpendicular to the following vectors $ 2\hat{i} + 2\hat{j}- k$ and $6\hat{i}-3\hat{j}+2k$ 

$(\overline{A} + \overline{B} )\times ( \overline{A} - \overline{B} )$ is

The vectors $\vec{A}=4\hat{i}+3\hat{j}+\hat{k}$ and $\vec{B}=12\hat{i}+9\hat{j}+3\hat{k}$ are parallel to each other.

The momentum of a particle is $\vec { P } =\vec { A } +\vec { B } { t }^{ 2 }$, where $\vec { A }$ and $\vec { B }$ are constant perpendicular vectors. The force acting on the particle when its acceleration is at ${45}^{o}$ with its velocity is

Find the projection of $ \vec A =2\hat { i } -\hat { j } +\hat { k } \quad on\quad \vec  B  =\quad \hat { i } -2\hat { j } +\hat { k }  $

The resultant of the two vector is having magnitude 2 and 3 is 1. What is their cross product 

The vector of  magnitude 18 which is perpendicular to both vectors $4\hat i-\hat j+3\hat k \,and  -2\hat i+\hat j-2\hat k$  is

The component of vector $2\ \hat {i}+3\hat {j}$ along vector $-\hat {j}+5\hat {i}$ is:

If $\vec {u},\vec {v}$ and $\vec {w}$ are three non-coplanar vectors, then
$(\vec {u}+\vec {v}-\vec {w}).(\vec {u}-\vec {v})\times (\vec {v}-\vec {w})$ equals

Let $\vec {a}$ and $\vec {b}$ to two unit vectors. If the vectors $\vec {c}=\hat {a}+2\hat {b}$ and $\vec {d}=5\hat {a}-4\hat {b}$ are perpendicular to each other, then teh angle between $\vec {a}$ and $\vec {b}$ is

Which of the following vector is perpendicular to the vector $A=2\hat{i}+3\hat{j}+4\hat{k}$?

Which of the following vector is perpendicular to the vector $\vec { A } =\hat { 2i } +\hat { 3j } +\hat { 4k } $?

Find a vector $\vec {x}$ which is perpendicular to both $\vec {A}$ and $\vec {B}$ but has magnitude equal to that of $\vec {B}$. Vector $\vec {A}=3\hat{i}-2 \hat {j} +\hat {k}$ and $\vec {B}=4\hat{i}+3 \hat {j} -2\hat {k}$

Three vectors $\vec A, \vec B$ and $\vec C$ satisfy the relation $\vec {A}\cdot \vec {B}=0$ and $\vec{A}\cdot \vec{C}=0$. The vector $A$ is parallel to :

A vector $\vec{A}$ is along +ve x-axis. Another vector $\vec{B}$ such that $\vec{A} \times \vec{B}=\vec{0}$ could be

If $\vec{A}=5 \hat {i}+7 \hat{j}-3 \hat {k}$ and $\vec{B}=15 \hat {i}+21 \hat{j}+a \hat {k}$ are parallel vectors then the value of $a$ is:

If $\vec{A}\times\vec{B}=\vec{C}$, then choose the incorrect option : [$\vec{A}$ and $\vec{B}$ are non zero vectors]

If $\overrightarrow a  + b + \overrightarrow c  = 0$ The angle between $\overrightarrow a \,\,and\,\,\overrightarrow b \,,b\,and\,\overrightarrow c \,and\,{150^0}\,\,and\,\,{120^0}$ respectively.The the magnitude of vectors $\overrightarrow a ,\overrightarrow b \,\,and\,\,\overrightarrow c $ are in ratio of .

If  $\vec { A } = 4 \vec { i } + 5 \vec { j } - 6 \vec { k }$  and  $\vec { B } = 2 \vec { i }  - 3 \vec { j } + 4 \vec { k }$  then  $( \vec { A } + \vec { B } ) \cdot (\vec { A } - \vec { B } )$  is

If the two given vectors $ 2 \hat i + 3 \hat j + 4 \hat k $ and $ 6 \hat i +  \alpha \hat j + \beta \hat k $ are parallel , the value of $ \alpha $ and $ \beta $ will be

If $\overrightarrow{A}=4\widehat{i}+6\widehat{j} $  and  $\overrightarrow{B}=2\widehat{i}+3\widehat{j}$ .Then :

If $  \overrightarrow{A} \times \overrightarrow{B}=0,$ $  \overrightarrow{B} \times \overrightarrow{C}=0, $then $  \overrightarrow{A} \times \overrightarrow{C}= $

Consider a vector $F=4\hat{i}-3\hat{j} $. Another vector which is perpendicular to $\vec F$ is:

Show that the vector is parallel to a vector $\displaystyle \vec{A}=\hat{i}-\hat{j}+2\hat{k}$ is parallel to a vector $\displaystyle \vec{B}=3\hat{i}-3\hat{j}+6\hat{k}.$

If $\vec{a}=x _1\hat {i}+y _1\hat {j}$ and $\vec{b}=x _2\hat {i}+y _2\hat {j}$. The condition that would make $\vec{a}$ and $\vec{b}$ parallel to each other is........... .

A vector $\bar{P} _{1}$ is along the positive x- axis. If its cross product with another vector $\bar{P} _{2}$ is zero, then $\bar{P} _{2}$ could be:

If three vectors satisfy the relation $ \overrightarrow A . \overrightarrow B = 0 $ and $ \overrightarrow A . \overrightarrow C = 0 $ , then $ \overrightarrow A $ can be parallel to

Consider the following statements A and B given below and identify the correct answer:
A) lf $\vec{\mathrm{A}}$ is a vector, then the magnitude of the vector is given by $\sqrt{\vec{A}\times \vec{A}}$
B) lf $\vec{a}=m\vec{b}$ where 'm' is a scalar, the value of 'm' is equal to $\frac{\vec{a} \cdot  \vec{b}}{b^{2}}$

lf vectors $\vec{\mathrm{A}}$ and $\vec{\mathrm{B}}$ are given by $\vec{\mathrm{A}}=5\hat{\mathrm{i}}+6\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and $\vec{\mathrm{B}}=6\hat{\mathrm{i}}-2\hat{\mathrm{j}}-6\hat{\mathrm{k}}$ then which of the following is/are correct?
$a)\vec{\mathrm{A}}$ and $\vec{\mathrm{B}}$ are mutually perpendicular
$\mathrm{b})$ Product of $\vec{\mathrm{A}}\times\vec{\mathrm{B}}$ is same as $\vec{\mathrm{B}}\times\vec{\mathrm{A}}$
$\mathrm{c})$ The magnitude of $\vec{\mathrm{A}}$ and $\vec{\mathrm{B}}$ are equal
$\mathrm{d})$ The magnitude of $\vec{\mathrm{A}}.\vec{\mathrm{B}}$ is zero

lf $\vec{a}=2\hat{i}+6n\hat{j}+m\hat{k}$ and $\vec{b}=\hat{i}+18\hat{j}+3\hat{k}$ are parallel to each other then the values of $m,n$ are:

$\vec{A}$ and $\vec{B}$ are two vectors in a plane at an angle of $60^{0}$ with each other. $\vec{C}$ is another vector perpendicular to the plane containing vectors $\vec{A}$ and $\vec{B}$. Which of the following relations is possible?

If $\vec{A} = 2\hat{i} + \hat{j}$ and $\vec{B} = \hat{i} - \hat{j}$, sketch vectors graphically and find the component of $\vec{A}$ along $\vec{B}$ and perpendicular to $\vec{B}$.

Given $\vec{A} = 2\hat{i} + p\hat{j} + q\hat{k}$ and $\vec{B}=5\hat{i}+7\hat{j} + 3\hat{k}$. If $\vec{A}|| \vec{B}$, then the values of $p$ and $q$ are, respectively,

If the two vectors $\vec{A} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} - n \hat{k}$ are perpendicular, then the value of $n$ is:-

Given $\overline { a } + \overline { b } + \vec { c } + \overline { d } = 0$ , which of the following statements is/are not a correct statement?