Example 23 - Chapter 11 Class 12 Three Dimensional Geometry
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.