Question

The area of the parallelogram is $4\sqrt{29}$ sq. unit. If one of adjacent sides is $3\overline{i}+4\overline{j}$, then the other side is

• A. $\overline{i}-4\overline{k}$
• B. $2\overline{i}+4\overline{k}$
• C. $-2\overline{j}-4\overline{k}$
• D. $2\overline{i}-4\overline{k}$

Answer 1

The correct option is D $2\overline{i}-4\overline{k}$

Area of Parallelogram is $|\overline{a}\times \overline{b}|=4\sqrt{29}$ ........(1)

Let one side be $\overline{a}=3\overline{i}+4\overline{j}$ , other side be $\overline{b}$

Now by verifying all options , only option D satisfy the equation (1) as follows,

$\overline{a}\times \overline{b}=\left[\begin{array}{ccc}i& j& k\\ 3& 4& 0\\ 2& 0& -4\end{array}\right]$

$=i(-16-0)-j(-12-0)+k(0-8)=-16i+12j-8k$

Now, $|\overline{a}\times \overline{b}|=\sqrt{256+144+64}$

$=\sqrt{464}=\sqrt{29\times 16}=4\sqrt{29}$