Answer
The triangle is right-angled.
Work Step by Step
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 the 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 sides form a right angle.
Hence, the triangle is a right triangle.
