Finding the Distance Between Two Points in Space

Find the distance between \(P_{1}=(1, 3,-2)\) and \(P_{2}=(2,-1,-3)\).

Solution \[ |P_{1}~P_{2}|=\sqrt{(2-1)^{2}+(-1-3)^{2}+(-3+2)^{2}}= \sqrt{1+16+1}=\sqrt{18}=3\sqrt{2}\qquad \]