If $|\overrightarrow A \times \overrightarrow B | = |\overrightarrow A \cdot \overrightarrow B |$,then the angle between $\overrightarrow A$ and $\overrightarrow B$ will be ........ $^o$.

$\overrightarrow{A}$ 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

The angle between the vectors $(\hat{i} + \hat{j})$ and $(\hat{j} + \hat{k})$ is ....... $^\circ$.

The diagonals of a parallelogram are $2\,\hat{i}$ and $2\,\hat{j}$. What is the area of the parallelogram in square units?

Three vectors $\vec a$,$\vec b$,and $\vec c$ satisfy the relations $\vec a \cdot \vec b = 0$ and $\vec a \cdot \vec c = 0$. The vector $\vec a$ is parallel to:

If $\vec{A} \times \vec{B} = \vec{0}$ and $\vec{B} \times \vec{C} = \vec{0}$,what is the angle between $\vec{A}$ and $\vec{C}$?