Answer
$|PQ|=6$
$|QR|=2\sqrt{10}$
$|RP|=6$
The triangle is isosceles.
Work Step by Step
The side lengths can be calculated using the distance formula:
$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2)}$
$|PQ|=\sqrt{(7-3)^2+(0+2)^2+(1+3)^2)}=6$
$|QR|=\sqrt{(1-7)^2+(2-0)^2+(1-1)^2)}=\sqrt{40}=2\sqrt{10}$
$|RP|=\sqrt{(3-1)^2+(-2-2)^2+(-3-1)^2)}=6$
Since two of the legs are the same length, the triangle is isosceles.