Question

The diagonals of a parallelogram are represented by $R_1=3\hat{i}+2\hat{j}-7\hat{k}$ and $R_2=5\hat{i}+6\hat{j}-3\hat{k}$. Find the area of the parallelogram.

Answer 1

Area of the parallelogram represented by the two vectors $=|\overrightarrow{A}\times \overrightarrow{B}|$

$=|(3\hat{i}+2\hat{j}-7\hat{k})\times (5\hat{i}+6\hat{j}-3\hat{k})|$

$=|36\hat{i}-26\hat{j}+8\hat{k}|$

$=\sqrt{{36}^2+{26}^2+8^2}$

$=\sqrt{2036}=45.12$ square unit