If $\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{Q}}$ , then which of the following is NOT correct?

1. $\hat{\mathrm{P}}=\hat{\mathrm{Q}}$

2. $\left|\overrightarrow{\mathrm{P}}\right|=\left|\overrightarrow{\mathrm{Q}}\right|$

3. $\mathrm{P}\hat{\mathrm{Q}}=\mathrm{Q}\hat{\mathrm{P}}$

4. $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}=\hat{\mathrm{P}}+\hat{\mathrm{Q}}$

Which of the following is a scalar quantity

1. Displacement

2. Electric field

3. Acceleration

4. Work

There are two force vectors, one of 5N and the other of 12N. At what angle should the two vectors be added to get the resultant vector of 17N, 7N, and 13N, respectively:

1. $0°, 180° \mathrm{and} 90°$

2. $0°, 90° \mathrm{and} 180°$

3. $0°, 90° \mathrm{and} 90°$

4. $180°, 0° \mathrm{and} 90°$

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