Question 1 :
If the vectors $\displaystyle \vec{P}= a\tilde{i}+a\hat{j}+3\hat{k}\:and\:\vec{Q}= a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other then the positive value of a is

Question 2 :
If A and B are two perpendicular vectors given by $\overline{A}=5\overline{i}+7\overline{j}+3\overline{k}$, and $4\overline{B}=2\overline{i}+2\overline{j}+c\overline{k}$, then the value of $\mathrm{c}$ is:<br/>

Question 3 :
If $a$ , $b$ and $c$ are three non-zero vectors such that $a.|b \times c| = 0$ and $b$ and $c$ are not parallel then $a$ , $b$ and $c$ are

Question 4 :
We can represent velocity vector as _______ and its magnitude as ________ .

Question 5 :
Given $\vec{P} = 3\hat{i} - 4\hat{j}$ , Which of the following is perpendicular to $\vec{P}$?

Question 7 :
The magnitude of vector product of two vectors $\overline{\mathrm{P}}\times\overline{\mathrm{Q}}$ may be:<br/>

Question 8 :
If a vector $2\widehat{i} + 3\widehat{j} +8\widehat{k}$ is perpendicular to the vector $4\widehat{i}-4\widehat{j}+a\widehat{k},$ then the value of $a$ is :<br>

Question 9 :
Given $\vec {F}=(4 \hat{i}-10 \hat {j})$ and $\vec {r}=(-5 \hat{i}-3 \hat {j})$, then compute torque.

Question 10 :
A force with components (-7, 4, 5) acts at the point (2, 4, -3). Find the magnitude of moment about the origin.<br>

Question 11 :
It is possible to have $ \underset{a}{\rightarrow}\times \underset{b}{\rightarrow}=\underset{a}{\rightarrow}.\underset{b}{\rightarrow} $ for some suitable seclection of $\underset{a}{\rightarrow} $ and $\underset{b}{\rightarrow} $ For example $\underset{a}{\rightarrow} $=$\underset{0}{\rightarrow} $ . The statement is

Question 12 :
If the resultant of two forces $P$ and $Q$ be equal in magnitude to one of the components $P$ and perpendicular to it in direction, then the value of $Q$ is <br/>

Question 13 :
Three forces $ \overrightarrow P $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are acting at a point in a plane. The angle between $ \overrightarrow P $ and $\overrightarrow Q $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are $ 150^{\circ} $ and $ 120^{\circ} $ respectively. Then for the equilibrium, forces $ \overrightarrow P $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are in the ratio :-

Question 14 :
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:

Question 15 :
Let a force $\displaystyle \vec{F}$ be acting on a body free to rotate about a point O and let $\displaystyle \vec{r}$ the position vector of any point P on the line of action of the force. Then torque $\displaystyle \vec{t}$ of this force about point O is defined as $\displaystyle \vec{t}= \vec{r}\times \vec{F}$<br>Given, $\displaystyle \vec{F}= \left ( 2\hat{i}+3\hat{j}-\hat{k} \right )N\:and\:\vec{r}= \left ( \hat{i}-\hat{j}+6\hat{k} \right )m$<br>Find the torque of this force.