Question

prove that the vectors A=3i+2j-2k,B=-1+3j+4k and c=4i-j-6k can form a triangle

Answer 1

you can too solve it using Martices.

Answer 2

take \(\vec A -\vec B\). you'll get \[(3 \mathbb i +2\mathbb j-2\mathbb k)-(-\mathbb i+3\mathbb j+4 \mathbb k)=4\mathbb i - \mathbb j -6\mathbb k=\vec C\]
so eventually you get \(\vec A -\vec B=\vec C\) or
\[\vec A=\vec B +\vec C\]
This a property when three vectors form a triangle

Answer 3

Using Matrix will be much easier