Show that $a=2i+2j+3k,b=3i+j-k,c=i-j-4k$ forms the sides of a triangle.

My attempt: $|a|=\sqrt{17},|b|=\sqrt{11},|c|=\sqrt{18}.$ Since $|c|<|a|+|b|$ using triangle inequality, we can say a,b,c form sides of a triangle.

I am not sure if my attempt is correct.

My attempt: $|a|=\sqrt{17},|b|=\sqrt{11},|c|=\sqrt{18}.$ Since $|c|<|a|+|b|$ using triangle inequality, we can say a,b,c form sides of a triangle.

I am not sure if my attempt is correct.