$\begin{array}{l}\text{\hspace{0.17em}If\hspace{0.17em}}|\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}|=\sqrt{3}\overrightarrow{\mathrm{A}}\cdot \overrightarrow{\mathrm{B}}\text{, then the value of\hspace{0.17em}}\\ |\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\text{\hspace{0.17em}is:\hspace{0.17em}}\end{array}$

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 the angle between the vector $\overrightarrow{\mathrm{A}}\text{\hspace{0.17em}and\hspace{0.17em}}\overrightarrow{\mathrm{B}}$ 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\(\sin\theta\)