Triangle formed by three lines whose direction ratios are $〈-1,1,1〉,〈1,\sqrt{2},0〉,〈1,1,0〉$ is

Suppose that the given lines form a triangle $ABC$ 

 Hence, 

$\begin{array}{c}\cos A=\frac{-1+\sqrt{2}}{\sqrt{1+1+1}\sqrt{1+2}}=\frac{\sqrt{2}-1}{3}\\ \cos B=\frac{1+\sqrt{2}}{\sqrt{1+2}\sqrt{1+1}}=\frac{\sqrt{2}+1}{\sqrt{6}}\\ \cos C=\frac{-1+1}{\sqrt{1+1}\sqrt{1+1+1}}=0\end{array}$            

Since $\cos C=0$,the measure one angle in the triangle is right angle, so that the triangle formed by the given lines is right angled triangle.