## Calculus 8th Edition

Suppose $a=PQ= (2,0,-4)-(1,-3,-2)= \lt 1,3,-2 \gt$ $b=QR=(6,-2,-5)-(2,0,-4)= \lt 4,-2,-1 \gt$ $c=RP=(1,-3,-2)-(6,-2,-5)= \lt -5,-1,3 \gt$ Now we will take dot product of $a$ and $b$. $a \cdot b= \lt 1,3,-2 \gt \cdot \lt 4,-2,-1 \gt=4-6+2=0$ Since the dot product of $a$ and $b$ is $0$ , this implies that $a \perp b$ or $PQ \perp QR$, so these two side form a right angle. Hence, the triangle is a right triangle.