6.8.10 Angle between two planes

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The angle between two given planes is same as the angle between their normals. Theorem . The acute angle θ between the two planes  r n and  r n is given by n n n n −      Proof If θ is the acute angle between two planes  r n and  r n , then θ is the acute angle between their normal vectors  n and  n . Therefore, n n n n n n n n ⇒         ... ( ) Remark (i) If two planes r n r n are perpendicular, then n n (ii) If the planes r n r n are parallel, then  , where λ is a scalar (iii) Equation of a plane parallel to the plane r n is r n k k ∈  Theorem . The acute angle θ between the planes a x b y c z a x b y c z is given by a a b b c c −      Fig. .

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