Two vectors $\vec{A}$ and $\vec{B}$ are at right angles to each other,when

If $|\vec{A} \times \vec{B}| = \sqrt{3} \vec{A} \cdot \vec{B}$,then what is the value of $|\vec{A} + \vec{B}|$?

If $\overrightarrow{A} = 2\widehat{i} - 2\widehat{j}$ and $\overrightarrow{B} = 2\widehat{k}$,then find the dot product $\overrightarrow{A} \cdot \overrightarrow{B}$.

The resultant of two vectors having magnitudes $2$ and $3$ is $1$. What is their cross product?

What will be the projection of vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ on vector $\vec{B} = \hat{i} + \hat{j}$?

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors given by $\overrightarrow{A} = 2\widehat{i} + 3\widehat{j}$ and $\overrightarrow{B} = \widehat{i} + \widehat{j}$. The magnitude of the component (projection) of $\overrightarrow{A}$ on $\overrightarrow{B}$ is