Question

If the area of the parallelogram with $\vec{a}$ and $\vec{b}$ as two adjacent sides is $15$ sq. units then the area of the parallelogram having $3\vec{a}+2\vec{b}$ and $\vec{a}+3\vec{b}$ as two adjacent sides in sq. units is

• A. 45
• B. 75
• C. 105
• D. 120

Answer 1

Answer: (C)

$|\vec{a}\times \vec{b}|=15$
$|(3\vec{a}+2\vec{b})\times (\vec{a}+3\vec{b})|$
$=|9(\vec{a}+\vec{b})\times 2(\vec{b}+\vec{a})|$
$=|7(\vec{a}\times \vec{b})|=7\times 15=105$