Answer
$d(P,Q)=\sqrt {(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$, $\sqrt {38}$, $(x-5)^2+(y-2)^2+(z-3)^2=9$
Work Step by Step
The formula to calculate the distance between two points in space is given by
$d(P,Q)=\sqrt {(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$ The point given in the figure has coordinates of P(5,2,3), the coordinates of the origin is (0,0,0) and the distance between them is then
$d(P,O)=\sqrt {(5-0)^2+(2-0)^2+(3-0)^2}=\sqrt {25+4+9}=\sqrt {38}$. The general equation of a sphere is given by $(x-h)^2+(y-k)^2+(z-l)^2=r^2$ where the center is at (h,k,l) and the radius is $r$. Thus the equation of the sphere centered at P with radius 3 is $(x-5)^2+(y-2)^2+(z-3)^2=9$
