d
અદીશ \(\mathop {\rm{A}}\limits^ \to  \,\, = \,\,2\hat i\,\, + \;\,3\hat j\,\, + \;\,\hat k\) અને અદીશ \(\mathop B\limits^ \to  \,\, = \,\,\hat i\,\, - \,\,\hat j\,\, + \;\,2\hat k\)

\(\vec A \) અને \(\vec B \) નો લંબ એકમ સદીશ \(\hat n\, = \,\,\frac{{\mathop A\limits^ \to  \,\, \times \,\,\mathop B\limits^ \to  }}{{|\mathop A\limits^ \to  \,\, \times \,\,\mathop B\limits^ \to  |}}\)

\(\,\,\mathop A\limits^ \to  \,\, \times \,\,\mathop B\limits^ \to  \,\, = \,\,\left| {\left. {\begin{array}{*{20}{c}}
{\hat i}&{\hat j}&{\hat k}\\
2&3&1\\
1&{ - 1}&2
\end{array}} \right|} \right.\,\, = \,\,\hat i\left( {6\,\, + \;\,1} \right)\,\, - \,\,\hat j\,\,\left( {4\,\, - \,\,1} \right)\,\, + \;\,\hat k\,\,\left( { - 2\,\, - \,\,3} \right)\,\, = \,\,7\hat i\,\, - \,\,3\hat j\,\, - \,\,5\hat k\)

\(\,|\mathop A\limits^ \to  \,\, \times \,\,\mathop B\limits^ \to  |\,\, = \,\,\sqrt {{7^2}\,\, + \;\,{{\left( { - 3} \right)}^2}\,\, + \;\,{{\left( { - 5} \right)}^2}} \,\, = \,\,\sqrt {83} \) એકમ 

\(\therefore \,\hat n\,\, = \,\,\frac{1}{{\sqrt {83} }}\,\,\left( {7\hat i\,\, - \,\,3\hat j\,\, - \,\,5k} \right)\)