question_answer

The spheres\[{{r}^{2}}+2{{u}_{1}}\,.\,r+2{{d}_{1}}=0\] and \[{{r}^{2}}+2{{u}_{2}}\,.\,r+2{{d}_{2}}=0\] cut orthogonally, if [AMU 1999]

A)            \[{{u}_{1}}\,.\,{{u}_{2}}=0\]     

B)            \[{{u}_{1}}+{{u}_{2}}=0\]

C)            \[{{u}_{1}}\,.\,{{u}_{2}}={{d}_{1}}+{{d}_{2}}\]

D)            \[({{u}_{1}}-{{u}_{2}})\,.\,({{u}_{1}}+{{u}_{2}})=d_{1}^{2}+d_{2}^{2}\]