Question

Two non-zero vectors are parallel if their vector product is

Answer 1

$\textbf{Concept used:}$

$\text{The vector product of two non-zero vectors }$

$\text{ \overrightarrow{a} and \overrightarrow{b} is}$

$\overrightarrow{a}{\times}\overrightarrow{b}=|\overrightarrow{a}|\;|\overrightarrow{b}|\;sin\theta\;\widehat{n}$

$\text{ \widehat{n} is the unit vector perpendicular to both \overrightarrow{a} and \overrightarrow{b} }$

$\text{Suppose the vectors are parallel}$

$\text{Then, \theta=0^{\circ} }$

$\overrightarrow{a}{\times}\overrightarrow{b}=|\overrightarrow{a}|\;|\overrightarrow{b}|\;sin\,0^{\circ}\;\widehat{n}$

$\overrightarrow{a}{\times}\overrightarrow{b}=|\overrightarrow{a}|\;|\overrightarrow{b}|(0)\widehat{n}$

$\implies\bf\overrightarrow{a}{\times}\overrightarrow{b}=\overrightarrow{0}$