Question 1 :
The magnitude of resultant of two equal forces is double the magnitude of either of forces. The angle between them is:
Question 3 :
If a vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $4\hat{j}-4\hat{i}+\alpha \hat{k}$, then the value of $\alpha$
Question 4 :
$\vec A$ and $\vec B$ are vectors, and $\theta$ is the angle between them. What can you do to maximize $\vec A \cdot \vec B$ ?<br/>I. Maximize the magnitude of A<br/>II. Maximize the magnitude of B<br/>III. Set to $90^o$
Question 5 :
$If\,{a^ \to } \times {b^ \to } = {c^ \to }\,and\,{b^ \to } \times {c^ \to } = {a^ \to },\,then$
Question 6 :
The dot product of vectors $\vec{A}=4 \hat {i}+3 \hat {j}-2 \hat {k}$ and $\vec{B}=2 \hat {i}- \hat {j}+4 \hat {k}$ is :<br/>
Question 7 :
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
Question 8 :
What is the value of $(\vec {P}+\vec {Q}) \times (\vec {P}-\vec {Q})$?
Question 9 :
Find a vector perpendicular to $i+2j$ magnitude of $3\sqrt 5 $
Question 10 :
The line of action of a force $\vec{F}=\begin{pmatrix}-3\hat {i}+\hat {j}+5\hat {k}\end{pmatrix}\;N$ passes through a point $(7,3,1)$. The moment of force $(\vec{\tau}=\vec{r}\times\vec{F})$ about the origin is given by
Question 11 :
If the scalar and vector products of two vector are $4\sqrt{3}$ and $144$ respectively, what is the angle between the two vectors?<br/>
Question 12 :
Given, $\displaystyle \vec { \omega } =2\overset { \wedge }{ k } $ and $\displaystyle \vec { r } =2\overset { \wedge }{ i } +2\overset { \wedge }{ j } $. Find the linear velocity.
Question 13 :
The vector $\vec{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and $\vec{Q}=a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other. The positive value of $a$ is
Question 14 :
The torque of force $\displaystyle \vec{F}= \left ( 2\hat{i}-3\hat{j}+4\hat{k} \right )$ N acting at the point $\displaystyle \vec{r}= \left ( 3\hat{i}+2\hat{j}+3\hat{k} \right )$ m about origin is (in N-m):
Question 16 :
If the angle between two vectors is $ 60^o $, then $ \dfrac { \vec A.\vec B }{ |\vec A \times \vec B | } $ is
Question 17 :
What is the angle between $(\vec {A} - \vec {B})$ and $(\vec {A}\times \vec {B})$?
Question 18 :
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 :
Question 19 : If the dot product of the two vectors of non-zero magnitude is zero then:<p></p>
Question 20 :
An electron is moving with speed $2\times10^{5}m/s$ along the positive $\mathrm{x}$-direction in the presence of magnetic induction $\overline{B}=(\overline{i}+4\overline{j}-3\overline{k})T$. The magnitude of the force experienced by the electron in newtons is $(\mathrm{e}=1.6\times 10^{-19}C)$<br>
Question 21 :
lf $\vec{\mathrm{A}}=4\mathrm{\hat i}+2\mathrm{\hat j}+6\mathrm{\hat k}$, set the following values in increasng order.<br/>a) $ \vec{\mathrm{A}}.\hat{i}$ <br/>b) $ \vec{\mathrm A}.\hat{j}$ <br/>c) $ \vec{\mathrm{A}}.\hat{\mathrm{k}}$<br/>
Question 22 :
$\mathrm{A}$ force $\vec{F}=2\hat{i}+4\hat{j}+\hat{k}$ acts on a body and produces a displacement of $\vec{S}=3\hat{i}+2\hat{j}+5\hat{k}$. Work done is:<br/>
Question 23 :
If a vector $ 2 \hat{i} + 3 \hat{j} + 8 \hat{k} $ is perpendicular to the vector $ 4 \hat{j} - 4 \hat {i} + \alpha \hat{k} .$ Then, the value of $ \alpha$ is :
Question 24 :
The angular velocity of a rotating body is $\vec{\omega}=4\hat{i}+\hat{j}-2\hat{k}$. The linear velocity of the body whose position vector is 2$\hat{i}+3\hat{j}-3\hat{k}$ is:<br/>
Question 25 :
A vector $ \vec{F} $ is acting along positiove $Y-$ axis. If the vector product with another vector $\vec{F_2}$ is zero then $\vec{F_2} $ could be :
Question 26 :
If $ \overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow C = \overrightarrow C \times \overrightarrow A $ then $ \overrightarrow A + \overrightarrow B + \overrightarrow C $ is equal to:
Question 27 :
The linear velocity of a rotating body is given by $\vec{v}=\vec{\omega}\times\vec{r}$, where $\vec{\omega}$ is the angular velocity and $\vec{r}$ is the radius vector. The angular velocity of a body is $\vec{\omega}=\hat{i}-2\hat{j}+2\hat{k}$ and the radius vector $\vec{r}=4\hat{j}-3\hat{k}$, then $\begin{vmatrix}\vec{v}\end{vmatrix}$ is:
Question 28 :
If $\displaystyle \vec{a}=\hat{i}+\hat{j}+\hat{k}$ & $\displaystyle \vec{b}=\hat{j}-\hat{k},$ then the vector $\displaystyle \vec{c}$ such that $\displaystyle \vec{a}.\vec{c}=3$ & $\displaystyle \vec{a}\times \vec{c}=\vec{b}$ is
Question 29 :
The maximum magnitude of cross product of two vectors is $12$ units and the maximum magnitude of their resultant in $7$ units, then their minimum resultant vector will be a:
