Question

The area $(insq.units)$ of the parallelogram whosed diagonals along the vectors $8\hat{i}-6\hat{j}$ and $3\hat{i}+4\hat{j}-12\hat{k}$, is:

• A. $20$
• B. $65$
• C. $52$
• D. $26$

Answer 1

Answer: (B)

$65$

Area of Parallelogram = $\frac{1}{2}|\overrightarrow{D_1}\times \overrightarrow{D_2}|$

$\to \frac{1}{2}(8\hat{i}-6\hat{j})\times (3\hat{i}+4\hat{j}-12\hat{k})$

$\to \frac{1}{2}|32\hat{k}+96\hat{j}+18\hat{k}+72\hat{i}|$

$\to |36\hat{i}+48\hat{j}+25\hat{k}|$

$\to \sqrt{{36}^2+{48}^2+{25}^2}=65sq.units$