Question

If vector$\left(\hat{i}+\hat{j}+\hat{k}\right)$ and $3\hat{i}$ form two sides of a triangle and the magnitude of area of triangle is $\frac{x}{\sqrt{y}}$, then x+y is
(x and y are prime numbers).

Answer 1

Area of triangle= $\frac{1}{2}\overrightarrow{A}\times \overrightarrow{B}=\frac{1}{2}\left(\hat{i}+\hat{j}+\hat{k}\right)\times 3\hat{i}=$
$\frac{1}{2}\left(-3\hat{k}+3\hat{j}\right)=\frac{3\sqrt{2}}{2}$
Given, area=$\frac{x}{\sqrt{y}}$
so, $\frac{3\sqrt{2}}{2}=\frac{x}{\sqrt{y}}$
on solving further
$x+y=5$