If the vectors $(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})$ and $3\hat{\mathbf{i}}$ form two sides of a triangle, the area of the triangle is

: Area of triangle =$\frac{1}{2}AB\sin \theta =\frac{|\mathbf{A}\times \mathbf{B}|}{2}$

$\mathbf{A}\times \mathbf{B}=(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\times 3\hat{\mathbf{i}}$

$=-3\hat{\mathbf{k}}+3\hat{\mathbf{j}}$

$|\mathbf{A}\times \mathbf{B}|=\sqrt{(-3{)}^2+(3{)}^2}$

$=3\sqrt{2}$

Area =$\frac{3\sqrt{2}}{2}=\frac{3}{\sqrt{2}}unit$