# Example 23 - Chapter 11 Class 12 Three Dimensional Geometry

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 23 Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y – 2z =5. Angle between two planes A1x + B1y + C1z = d1 and A2x + B2y + C2z = d2 is given by cos θ = 𝑨𝟏 𝑨𝟐 + 𝑩𝟏 𝑩𝟐 + 𝑪𝟏 𝑪𝟐 𝑨𝟏𝟐 + 𝑩𝟏𝟐 + 𝑪𝟏𝟐 𝑨𝟐𝟐 + 𝑩𝟐𝟐 + 𝑪𝟐𝟐 Given the two planes are So, cos θ = 3 × 2 + −6 × 2 + (2 × −2) 32 + (−6)2 + 22 22 + 22 + (−2)2 = 6 + −12 + (−4) 9 + 36 + 4 × 4 + 4 + 4 = −10 49 × 12 = −107 × 4×3 = 107 × 2 × 3 = 57 3 = 57 3 × 3 3 = 5 321 So, cos θ = 5 321 ∴ θ = 𝒄𝒐𝒔−𝟏 𝟓 𝟑𝟐𝟏 Therefore, the angle between the two planes is 𝑐𝑜𝑠−1 5 321

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Chapter 11 Class 12 Three Dimensional Geometry

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.