Question

If one side of the square is represented by $3\hat{i}+4\hat{j}+5\hat{k}$, then the area(in sq. units) of the square is

Answer 1

Let, $\overrightarrow{a}=3\hat{i}+4\hat{j}+5\hat{k}$
$\Rightarrow |\overrightarrow{a}|=\sqrt{3^2+4^2+5^2}=5\sqrt{2}$
Thus the length of side of square is $5\sqrt{2}$
Hence, area of square is $(5\sqrt{2}{)}^2=50$ sq. units