Angle Between Two Planes
Category : JEE Main & Advanced
Angle between the planes is defined as angle between normals to the planes drawn from any point. Angle between the planes \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z+{{d}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z+{{d}_{2}}=0\] is \[{{\cos }^{-1}}\left( \frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{(a_{1}^{2}+b_{1}^{2}+c_{1}^{2})(a_{2}^{2}+b_{2}^{2}+c_{2}^{2})}} \right)\]
(i) If \[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}=0\], then the planes are perpendicular to each other.
(ii) If \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\], then the planes are parallel to each other.
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