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]

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

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

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

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

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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]

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