Question 1 :
$\vec A$ 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 2 :
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 3 :
Assertion: $\vec A \times \vec B$ is perpendicular to both $\vec A + \vec B$ as well as $\vec A -\vec B$ Reason: $\vec A +\vec B$ as wll as $\vec A -\vec B$ lie in the plane containing $\vec A$ and $\vec B$, but $\vec A \times \vec B$ lies perpendicular to the plane containing $\vec A $ and $\vec B$

Question 5 :
The magnitude of resultant of two equal forces is double the magnitude of either of forces. The angle between them is:

Question 6 :
The value of $ (\bar { A } +\bar { B } )\times (\bar { A } -\bar { B } )$ is

Question 7 :
If vectors $ A=cos \omega t \hat { i } +sin\quad \hat { j } $ and $ B =cos \dfrac { \omega t }{ 2 } \hat { i } +sin \frac { \omega t }{ 2 } \hat { j } $ are functions of time, then the value of t at which they are orthogonal to each other

Question 8 :
Given $\vec {F}=(4 \hat{i}-10 \hat {j})$ and $\vec {r}=(-5 \hat{i}-3 \hat {j})$, then compute torque.

Question 9 :
A force $6 \hat{i}+3 \hat {j}+ \hat{k}$ N displaces a particle from $A(0,3,2)$ to $B(5,1,6)$. Find the work done.

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 :
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

Question 12 :
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 13 :
The position vector of a particle is given by $\vec{r}=1.2t\hat {i}+0.9t^2\hat {j}- 0.6(t^3-1)\hat {k}$ where $t$ is the time in seconds from the start of motion and where $\vec{r}$ is expressed in metres. <br/>Determine the power $\begin{pmatrix}P=\vec{F}.\vec{v}\end{pmatrix}$ in watts produced by the force $\vec{F}=\begin{pmatrix}60\hat {i}-25\hat {j}-40\hat {k}\end{pmatrix}N$ which is acting on the particle at time $t=4$ seconds.

Question 14 :
If $\vec A=3\hat i+4\hat j$ and $\vec B=6\hat i+8\hat j$ and A and B are the magnitudes of $\vec A$ and $\vec B$, then which of the following is not true?

Question 15 :
If $\overrightarrow{P}$ is directly vertically upwards and $\overrightarrow{Q}$ is directed towards north then direction of $\overrightarrow{P} \times \overrightarrow{Q}$ vector is directed towards :

Question 16 :
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 17 :
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 18 :
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 19 :
Force acting on a particle is $\begin{pmatrix}2\hat {i}+3\hat {j}\end{pmatrix}N$. Work done by this force is zero, when the particle is moved on the line $3y+kx=5$. Here value of $k$ is<br>

Question 20 :
If $\displaystyle \vec{a}=\hat{i}+\hat{j}+\hat{k}$ &amp; $\displaystyle \vec{b}=\hat{j}-\hat{k},$ then the vector $\displaystyle \vec{c}$ such that $\displaystyle \vec{a}.\vec{c}=3$ &amp; $\displaystyle \vec{a}\times \vec{c}=\vec{b}$ is