If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:

1. 90°

2. 45° 

3. 180° 

4. 0°

Six vectors $\overrightarrow{a} through \overrightarrow{f}$ have the directions as indicated in the figure. Which of the following statements may be true?

1. $\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{-f}$                       
2. $\overrightarrow{d}+\overrightarrow{c}=\overrightarrow{f}$
3. $\overrightarrow{d}+\overrightarrow{e}=\overrightarrow{f}$                       
4. $\overrightarrow{b}+\overrightarrow{e}=\overrightarrow{f}$

Assertion: The graph between P and Q is a straight line when P/Q is constant.
Reason: The straight-line graph means that P is proportional to Q or P is equal to a constant multiplied by Q.

Which one, of the following statements, is correct?
1. If both the assertion and the reason are true, and the reason is the correct explanation of the assertion.
2. If both the assertion and the reason are true but the reason is not the correct explanation of the assertion.
3. If the assertion is true but the reason is false.
4. If the assertion and reason are both false

In the given figure

1.  Angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ is $110°$

2.  Angle between $\overrightarrow{\mathrm{C}}$ and $\overrightarrow{\mathrm{D}}$ is $60°$

3.  Angle between $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$ is $110°$

4.  Angle between $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$ is $70°$

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

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.  $\sqrt{41} \mathrm{units}$

A body is moving according to the equation $\mathrm{x}=\mathrm{at}+{\mathrm{bt}}^2-{\mathrm{ct}}^3$ where x represents displacement and a, b and c are constants. The acceleration of the body is: (\(Given: a=\frac{d^2x}{dt^2}\))

1.  $\mathrm{a}+2\mathrm{bt}$

2.  $2\mathrm{b}+6\mathrm{ct}$

3.  $2\mathrm{b}-6\mathrm{ct}$

4.  $3\mathrm{b}-6{\mathrm{ct}}^2$

If \(\vec{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. \(x\vec{a}\) is a vector in the direction of \(\vec{a}\)
2. \(x\vec{a}\) is a vector collinear to \(\vec{a}\)
3. \(x\vec{a}\) and \(\vec{a}\) have independent directions
4. \(x\vec{a}\) is a vector perpendicular to \(\vec{a}\)

$\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are two vectors and θ is the angle between them. If $\left|\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}\right|=\sqrt{3}\left(\overrightarrow{A}.\overrightarrow{B}\right)$, then the value of θ will be:

1. 60^o

2. 45^o

3. 30^o

4. 90^o