Question

If the area of the parallelogram with $\vec {a}$ and $\vec {b}$ as two adjacent sides is $15\, sq.\space units$,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. unit is

• A. 45
• B. 75
• C. 105
• D. 120

Answer 1

Answer: (C)

105

Answer 2

The correct answer is C:105
We know, if $\vec{a}$ and $\vec{b}$ are two adjacent sides of a parallelogram, then
Area $= | \vec{a} \times \vec{b}| = 15$ (given) $\dots(i)$
If the sides are $(3 \; \vec{a} + 2 \vec{b})$ and $( \vec{a} + 3 \vec{b})$, then
Area of parallelogram
$= \left|\left(3 \vec{a} +2\vec{b}\right) \times\left(\vec{a} + 3\vec{b}\right)\right|$
$= \left|7 \left(\vec{a} \times\vec{b}\right)\right|$
$=7\left|\vec{a} \times\vec{b}\right|$
$= 7 \times15$ (From (i))
$= 105$ sq unit