The line segment $[ \mathrm { PQ } ]$ with endpoints $P ( 8 | - 5 | 1 )$ and $Q$ is a diameter of a sphere with center $M ( 5 | - 1 | 1 )$. Calculate the coordinates of $Q$ and show that the point $R ( 9 | - 1 | 4 )$ lies on the sphere.
The line segment $[ \mathrm { PQ } ]$ with endpoints $P ( 8 | - 5 | 1 )$ and $Q$ is a diameter of a sphere with center $M ( 5 | - 1 | 1 )$.
Calculate the coordinates of $Q$ and show that the point $R ( 9 | - 1 | 4 )$ lies on the sphere.