If the area of the parallelogram with \(\bar{a}\) and \(\bar{b}\) as two adjacent sides is 16 sq. units, then the area of the parallelogram having \(3 \bar{a}+2 \bar{b}\) and \(\overline{\mathrm{a}}+3 \overline{\mathrm{b}}\) as two adjacent sides (in sq. units) is

Area of the parallelogram with \(\bar{a}\) and \(\bar{b}\) as two adjacent sides is \(|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|\)
\(\therefore \quad|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=16\)
\(\therefore\) Area of the required parallelogram
\(\begin{aligned}
& =|(3 \overline{\mathrm{a}}+2 \overline{\mathrm{b}}) \times(\overline{\mathrm{a}}+3 \overline{\mathrm{b}})| \\
& =|3(\overline{\mathrm{a}} \times \overline{\mathrm{a}})+9(\overline{\mathrm{a}} \times \overline{\mathrm{b}})+2(\overline{\mathrm{b}} \times \overline{\mathrm{a}})+(\overline{\mathrm{b}} \times \overline{\mathrm{b}})| \\
& =0+9|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|-2|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|+0 \\
& =7|\overline{\mathrm{a}} \times \overline{\mathrm{b}}| \\
& =7 \times 16 \\
& =112
\end{aligned}\)