Question

If  \[\vec{c}\] is a unit vector perpendicular to the vectors \[\vec{a} \text{ and } \vec{b} ,\]  write another unit vector perpendicular to \[\vec{a} \text{ and }  \vec{b} .\]

 

 

 

Answer 1

\[\vec{c} \text{ is a unit vector perpendicular to both } \vec{a} \text{ and }  \vec{b} .\]

\[\Rightarrow \vec{c} =\frac{\vec{a} \times \vec{b}}{\left| \vec{a} \times \vec{b} \right|}\]

\[\Rightarrow- \vec{c} =\frac{\vec{b} \times \vec{a}}{\left| \vec{a} \times \vec{b} \right|}\]

\[\text{ Therefore,}  - \vec{c} \text{ is perpendicular to }  \vec{b} \text{ and }  \vec{a .} \]

\[\text{ Thus } , - \vec{c} \text{ is another unit vector perpendicular to }  \vec{a} \text{ and } \vec{b .}\]