Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Statement 1 - Let $A(\hat{i}+\hat{j}+\hat{k})$ and $B(\hat{i}-\hat{j}+\hat{k})$ be two points. Then the point $P(2\hat{i}+$ $3\hat{j}+\hat{k})$ lies exterior to the sphere with $AB$ as one of its diameters.

Statement 2 - If $A$ and $B$ are any two points and $P$ is a point in space such that $\overrightarrow{PA}\cdot \overrightarrow{PB}>0$, then the point $P$ lies exterior to the sphere with $AB$ as one of its diameters.