The value of unit vector in the direction of vector $\mathrm{A}=5 \hat{\mathrm{i}}-12 \hat{\mathrm{j}}$, is -

1. $\hat{\mathrm{i}}$

2. $\hat{\mathrm{j}}$

3. $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)/13$

4. $\left(5\hat{\mathrm{i}}-12\hat{\mathrm{j}}\right)/13$

A child pulls a box with a force of $200 \mathrm{N}$ at an angle of $60°$above the horizontal. Then the horizontal and vertical components of the force will be:
              

1. 100 N, 175 N

2.  86.6 N, 100 N  

3.  100 N, 86.6 N

4. 100 N, 0 N

A man rows a boat at a speed of $18 \mathrm{km}/\mathrm{hr}$ in the northwest direction. The shoreline makes an angle of $15°$ south of west. The component of the velocity of the boat along the shoreline is:

1.  $9 \mathrm{km}/\mathrm{hr}$

2.  $18\frac{\sqrt{3}}{2} \mathrm{km}/\mathrm{hr}$

3.  $18 \cos 15° \mathrm{km}/\mathrm{hr}$

4.  $18 \cos 75° \mathrm{km}/\mathrm{hr}$

A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is:

1. $5\left(\hat{\mathrm{i}}-2\hat{\mathrm{j}}\right)$

2. $5\left(4\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right)$

3. $0.6\hat{\mathrm{i}}+0.8\hat{\mathrm{j}}$

4. $6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$

If the angle between the unit vectors $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ is $60°$, then $|\hat{\mathrm{a}}-\hat{\mathrm{b}}|$ is :

(1)  0

(2)  1

(3)  2

(4)  4

For the figure -

1.  A+B=C

2.  B+C=A

3.  C+A=B

4.  A+B+C=0

Two constant forces ${\overrightarrow{\mathrm{F}}}_1=2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+3\hat{\mathrm{k}} \left(\mathrm{N}\right)$ and ${\overrightarrow{\mathrm{F}}}_2=\hat{\mathrm{i}}+\hat{\mathrm{j}}-2\hat{\mathrm{k}} \left(\mathrm{N}\right)$ act on a body and displace it from the position ${\overrightarrow{\mathrm{r}}}_1=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-2\hat{\mathrm{k}} \left(\mathrm{m}\right)$ to the position ${\overrightarrow{\mathrm{r}}}_2=7\hat{\mathrm{i}}+10\hat{\mathrm{j}}+5\hat{\mathrm{k}} \left(\mathrm{m}\right)$. What is the work done W? $[Given : W =\overrightarrow{F}.∆\overrightarrow{r}]$

(A)  9 Joule

(B)  41 Joule

(C)  -3 Joule

(D)  None of these

The angle that the vector $\mathrm{A}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}$ makes with the y-axis is:

(1)  ${\tan }^{-1} 3/2$

(2)  ${\tan }^{-1} 2/3$

(3)  ${\sin }^{-1} 2/3$

(4)  ${\cos }^{-1} 3/2$

A vector A points, vertically upward and, B points towards north. The vector product $\mathrm{A}\times \mathrm{B}$ is -

1.  along west

2.  along east

3.  zero

4.  vertically downward

The linear velocity of a rotating body is given by $\overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{\omega }}\times \overrightarrow{\mathrm{r}}$, where $\mathrm{\omega }$ is the angular velocity and r is the radius vector. The angular velocity of a body, $\overrightarrow{\mathrm{\omega }}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and their radius vector is  $\overrightarrow{\mathrm{r}}=4\hat{\mathrm{j}}-3\hat{\mathrm{k}}, \mathrm{then\; value\; of} \left|\overrightarrow{\mathrm{v}}\right|$ will be:

1.  $\sqrt{29} \mathrm{units}$

2.  $31 \mathrm{units}$

3.  $\sqrt{37} \mathrm{units}$

4.  $\sqrt{41} \mathrm{units}$