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Two constant forces ${\mathrm{F}}_1=2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+3\hat{\mathrm{k}} \left(\mathrm{N}\right)$ and ${\mathrm{F}}_2=\hat{\mathrm{i}}+\hat{\mathrm{j}} + \hat{\mathrm{k}}$ on a body and displace it from the position ${\mathrm{r}}_1=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-2\hat{\mathrm{k}} \left(\mathrm{m}\right)$ to the position ${\mathrm{r}}_2=7\hat{\mathrm{i}}+10\hat{\mathrm{j}}+5\hat{\mathrm{k}} \left(\mathrm{m}\right)$. What is the work done?
1.  30 Joule
2.  41 Joule
3.  -3 Joule
4.  None of these

Two vectors $\mathrm{P}=2\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}+2\hat{\mathrm{k}} \mathrm{and} \mathrm{Q}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}} \mathrm{will}$ be perpendicular if-
1.  b=0
2.  b=1
3.  b=2
4.  b=-4

Angle that the vector $\mathrm{A}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}$ makes with y-axis is-
1.  ${\tan }^{-1} 3/2$
2.  ${\tan }^{-1} 2/3$
3.  ${\sin }^{-1} 2/3$
4.  ${\cos }^{-1} 3/2$

The linear velocity of a rotating body is given by v=w$\times$r, where w is the angular velocity and r is the radius vector. The angular velocity of a body $\mathrm{w}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and their radius vector $\mathrm{r}=4\hat{\mathrm{j}}-3\hat{\mathrm{k}}, \left|\mathrm{v}\right|$ is-
1.  $\sqrt{29}$ units
2.  31 units
3.  $\sqrt{37}$ units
4.  $\sqrt{41}$ units

Given the vectors
$\overrightarrow{\mathrm{A}}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-\hat{\mathrm{k}}$
$\overrightarrow{\mathrm{B}}=3\hat{\mathrm{i}}-2\hat{\mathrm{j}}-2\hat{\mathrm{k}}$
$\& \overrightarrow{\mathrm{C}}=\mathrm{p}\hat{\mathrm{i}}+\mathrm{p}\hat{\mathrm{j}}+2\mathrm{p}\hat{\mathrm{k}}$
Find the angle between $\left(\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right) \& \overrightarrow{\mathrm{C}}$
1.  $\mathrm{\theta }={\cos }^{-1}\left(\frac{2}{\sqrt{3}}\right)$
2.  $\mathrm{\theta }={\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$
3.  $\mathrm{\theta }={\cos }^{-1}\left(\frac{\sqrt{2}}{3}\right)$
4.  none of these

Component of $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ perpendicular to $\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and in the same plane as that of $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ is:
1. $\frac{1}{2}\left(\hat{\mathrm{j}}-\hat{\mathrm{i}}\right)$
2. $\frac{3}{2}\left(\hat{\mathrm{j}}-\hat{\mathrm{i}}\right)$
3. $\frac{5}{2}\left(\hat{\mathrm{j}}-\hat{\mathrm{i}}\right)$
4. $\frac{7}{2}\left(\hat{\mathrm{j}}-\hat{\mathrm{i}}\right)$