b
જ્યારે \(\vec A \) અને \(\vec B \) સમાંતરબાજુ ચતુષ્કોણના વિકર્ણ હોય ત્યારે  સમાંતરબાજુ ચતુષ્કોણનું ક્ષેત્રફળ \( = \frac{1}{2} |\mathop A\limits^ \to  \times \mathop B\limits^ \to  | \)

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

\( = \frac{1}{2}|\mathop {{\rm{ }}A}\limits^ \to   \times \mathop {{\rm{ }}B}\limits^ \to  |=\) \({\hat i\left\{ {\left. {\left( { - 4} \right)\left( { - 1} \right) - \left( 3 \right)\left( { - 2} \right)} \right\}} \right. - \hat j\left\{ {\left. {\left( 5 \right)\left( { - 1} \right) - \left( 3 \right)\left( 3 \right)} \right\} + \hat k\left\{ {\left. {\left( 5 \right)\left( { - 2} \right) - \left( { - 4} \right)\left( 3 \right)} \right\}} \right.} \right.}\) \({ = 10\hat i + 14\hat j + 2\hat k}\) \({|\mathop A\limits^ \to   \times \mathop B\limits^ \to  | = \sqrt {{{\left( {10} \right)}^2} + {{\left( {14} \right)}^2} + {{\left( 2 \right)}^2}}  = \sqrt {300} }\) 

\(\frac{1}{2} |\mathop A\limits^ \to  \times \mathop B\limits^ \to  | \Rightarrow \frac{1}{2} \times 10\sqrt 3 = 5\sqrt 3 \)