$\begin{array}{l}\text{ If }|\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}|=\sqrt{3}\overrightarrow{\mathrm{A}}\cdot \overrightarrow{\mathrm{B}}\text{, then the value of }\\ |\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\text{ is: }\end{array}$

1. ${({\mathrm{A}}^2+{\mathrm{B}}^2+\frac{\mathrm{AB}}{\sqrt{3}})}^{1/2}$

2. A+B

3. ${({\mathrm{A}}^2+{\mathrm{B}}^2+\sqrt{3}\mathrm{AB})}^{1/2}$

4. ${({\mathrm{A}}^2+{\mathrm{B}}^2+\mathrm{AB})}^{1/2}$

If  $| \overrightarrow{A} + \overrightarrow{B} | = \left|\overrightarrow{A}\right| = | \overrightarrow{B}|$ then angle between A and B will be :- 

1.  $90°$

2. $120°$

3. $0°$

4. $60°$

The vector sum of two forces is perpendicular to their vector difference. In this case, the two forces: 

1. Are equal

2. Have the same magnitude

3. Are not equal in magnitude

4. Cannot be predicted

If the angle between the vector $\overrightarrow{\mathrm{A}}\text{ and }\overrightarrow{\mathrm{B}}$ is θ, the value of the product $(\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{A}})\cdot \overrightarrow{\mathrm{A}}$ is equal to

1. zero

2. BA²sinθcosθ

3. BA²cosθ

4. BA²sinθ

If a vector ($2\hat{\mathrm{i}}+3\hat{j}+8\hat{k}$) is perpendicular to the vector ($4\hat{\mathrm{i}}-4\hat{j}+\mathrm{\alpha }\hat{k}$), then the value of $\mathrm{\alpha \; is}$

1. -1

2. $-\frac{1}{2}$

3. $\frac{1}{2}$

4. 1

The vectors $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ are such that: $\left|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}\right|=\left|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right|$.
The angle between the two vectors is:

1. 90^o

2. 60^o

3. 75^o

4. 45^o

$\overrightarrow{\mathrm{A}}$ 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

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is 
                 

1.  $0.5 \mathrm{N}$

2.  $1.5 \mathrm{N}$

3.  $\frac{\sqrt{3}}{4} \mathrm{N}$

4.  $\sqrt{3} \mathrm{N}$

Six vectors $\overrightarrow{\mathrm{a}}$ through $\overrightarrow{\mathrm{f}}$ have the magnitudes and directions indicated in the figure. Which of the following statements is true? 

1. $\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{f}}$

2. $\overrightarrow{\mathrm{d}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{f}}$

3. $\overrightarrow{\mathrm{d}}+\overrightarrow{\mathrm{e}}=\overrightarrow{\mathrm{f}}$

4. $\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{e}}=\overrightarrow{\mathrm{f}}$

If vectors $\overrightarrow{\mathrm{A}}=\mathrm{cos\omega t}\hat{\mathrm{i}}+\mathrm{sin\omega t}\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=\cos \frac{\mathrm{\omega t}}{2}\hat{\mathrm{i}}+\sin \frac{\mathrm{\omega t}}{2}\hat{\mathrm{j}}$ are functions of time. Then, at what value of t are they orthogonal to one another?

1. $\mathrm{t}=\frac{\mathrm{\pi }}{4\mathrm{\omega }}$

2. $\mathrm{t}=\frac{\mathrm{\pi }}{2\mathrm{\omega }}$

3. $\mathrm{t}=\frac{\mathrm{\pi }}{\mathrm{\omega }}$

4. $\mathrm{t}=0$