## Thomas' Calculus 13th Edition

$7$
Formula to find the distance between two points is $|PQ|=\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}$ Let us consider $P=(1,4,5)$ and $Q=(4,-2,7)$ Thus, $|PQ|=\sqrt{(4-1)^2+(-2-4)^2+(7-5)^2}=\sqrt{3^2+(-6)^2+(2)^2}$ or, $|PQ|=\sqrt {9+36+4}=\sqrt{49}=7$