$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ nonzero constant. Which of the following expressions is true for $\vec{A}$ $?$
$\overrightarrow{ A }\cdot \overrightarrow{ A }=0$
$\overrightarrow{ A } \times \overrightarrow{ A }<0$
$\overrightarrow{ A } \times \overrightarrow{ A }=0$
$\overrightarrow{ A } \times \overrightarrow{ A }>0$
$\hat i.\left( {\hat j \times \,\,\hat k} \right) + \;\,\hat j\,.\,\left( {\hat k \times \hat i} \right) + \hat k.\left( {\hat i \times \hat j} \right)=$
Write the necessary condition for the scalar product of two mutually perpendicular vectors.
Write the distributive law for the product of two vectors.