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

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

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 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

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

1. zero

2. BA²\(\sin\theta \cos \theta\)

3. BA²\(\cos\theta\)

4. BA²\(\sin\theta\)