Angle of Intersection of Two Spheres
Category : JEE Main & Advanced
If the angle of intersection of two spheres is a right angle, the spheres are said to be orthogonal.
Condition for orthogonality of two spheres :
Let the equation of the two spheres be
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2ux+2vy+2wz+d=0\] .....(i)
and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2{u}'x+2{v}'y+2{w}'z+{d}'=0\] .....(ii)
If the sphere (i) and (ii) cut orthogonally, then \[2u{u}'+2v{v}'+2w{w}'=d+{d}',\] which is the required condition.
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