HCU MCA 2015 Paper

Consider the following statements about the locus of the point whose position vector $\overrightarrow{\mathrm{r}}$ satisfying $\left(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}\right).\overrightarrow{\mathrm{r}}=\frac{1}{2}\left({\mathrm{a}}^2-{\mathrm{b}}^2\right),$ where$\overrightarrow{\mathrm{a}}\mathrm{and}\overrightarrow{\mathrm{b}}$ are constant vectors with magnitudes ‘a’ and ‘b’ respectively.
$\left(\mathrm{i}\right)$ the locus is a plane passing through $\frac{1}{2}\left(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}\right)$.
$\left(\mathrm{ii}\right)$ the locus is a plane perpendicular to ($\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}$).
$\left(\mathrm{iii}\right)$ the locus is a sphere of radius ${\mathrm{a}}^2-{\mathrm{b}}^2.$
Which of the following is correct ?