If $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ a unit vector perpendicular to both $\overrightarrow A $ and $\overrightarrow B $ will be

A vector $\overrightarrow A $ points vertically upward and $\overrightarrow B $points towards north. The vector product $\overrightarrow A \times \overrightarrow B $ is

$\hat i.\left( {\hat j \times \,\,\hat k} \right) + \;\,\hat j\,.\,\left( {\hat k \times \hat i} \right) + \hat k.\left( {\hat i \times \hat j} \right)=$

The angle between the vectors $\overrightarrow A $ and $\overrightarrow B $ is $\theta .$ The value of the triple product $\overrightarrow A \,.\,(\overrightarrow B \times \overrightarrow A \,)$ is

If $|\vec A \times \vec B| = \sqrt 3 \vec A.\vec B,$ then the value of$|\vec A + \vec B|$ is

$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ nonzero constant. Which of the following expressions is true for $\vec{A}$ $?$