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 $