If $\overrightarrow{\mathrm{A}}=4\hat{\mathrm{i}}-3\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$ then magnitude and direction of $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ will be

1. $5, {\tan }^{-1}(3/4)$

2. $5\sqrt{5}, {\tan }^{-1}(1/2)$

3. $10, {\tan }^{-1}\left(5\right)$

4. $25, {\tan }^{-1}(3/4)$

If a particle moves from point P(2,3,5) to point Q(3,4,5). Its displacement vector be

1. $\hat{\mathrm{i}}+\hat{\mathrm{j}}+10\hat{\mathrm{k}}$

2. $\hat{\mathrm{i}}+\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

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

4. $2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+6\hat{\mathrm{k}}$

If vectors $\hat{\mathrm{i}}-3\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ and $\hat{\mathrm{i}}-3\hat{\mathrm{j}}-\mathrm{\alpha }\hat{\mathrm{k}}$ are equal vectors, then the value of $\mathrm{\alpha }$ is:

1. -5

2. 2

3. -3

4. 4

A plane is revolving around the earth with a speed of 100 km/hr at a constant height from the surface of the earth. The change in the velocity as it travels half-circle is:

1. 200 km/hr

2. 150 km/hr

3. $100\sqrt{2}$ km/hr

4. 0

A particle moves from position null to $(11\hat{\mathrm{i}}+11\hat{\mathrm{j}}+15\hat{\mathrm{k}})$ due to a uniform force of $(4\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}})$N. If the displacement is in m, then the work done will be: (Given: \(W=\vec{F}.\vec{S}\))

1. 100 J

2. 200 J

3. 300 J

4. 250 J

If for two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$, $\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}=0$, then the vectors:

1. are perpendicular to each other.

2. are parallel to each other.

3. act at an angle of $60°.$

4. act at an angle of $30°.$

When $\overrightarrow{\mathrm{A}}.\overrightarrow{\mathrm{B}}=-\left|\mathrm{A}\right|\left|\mathrm{B}\right|$, then

1. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are perpendicular to each other

2. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ act in the same direction

3. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ act in the opposite direction

4. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ can act in any direction

The dot product of two mutual perpendicular vector is:

1. 0

2. 1

3. $\infty$

4. None of the above

Current in a circuit is given by $i =3t^2+2t$. Find charge that crosses a cross-section from time t=0 to t=2 sec.

1. 12 C

2. 10 C

3. 8 C

4. 2 C

Let $\mathrm{\theta }$ be the angle between vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$. Which of the following figures correctly represents the angle $\mathrm{\theta }$?
1. 

2. 

3.  

4.