Question

The diagonals of a parallelogram are represented by vectors $\vec{p}=5 \hat{i}-4 \hat{j}+3 \hat{k}$ and $\vec{q}=3 \hat{i}+2 \hat{j}-k .$ Then the area of the parallelogram is

• A. $\sqrt{171}$ units
• B. $\sqrt{72}$ units
• C. 171 units
• D. 72 units

Answer 1

Answer: (A)

Area of parallelogram $=\frac{1}{2} \mid \vec{p} \times \vec{q}$
$=\frac{1}{2} \mid(5 \hat{i}-4 \hat{j}+3 \hat{k}) \times(3 \hat{i}+2 \hat{j}-\hat{k})$
$=\frac{1}{2}|-2 \hat{i}+14 \hat{j}+22 \hat{k}|=\frac{\sqrt{684}}{2}=\sqrt{171}$ units