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Example 22 - Find angle between two planes using vector method - Angle between two planes

Example 22 - Chapter 11 Class 12 Three Dimensional Geometry - Part 2

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Example 22 Find the angle between the two planes 2x + y 2z = 5 and 3x 6y 2z = 7 using vector method. Angle between two planes . ( 1) = d1 and .( 2) = d2 is given by cos = |(( ) . ( ) )/|( ) ||( ) | | Given, the two planes are 2x + y 2z = 5 Comparing with A1x + B1y + C1z = d1 Direction ratios of normal = 2, 1, 2 ( 1) = 2 + 1 2 Magnitude of ( 1) = (22+12+( 2)2) |( 1) |= (4+1+4) = 9 = 3 3x 6y 2z = 7 Comparing with A2x + B2y + C2z = d2 Direction ratios of normal = 3, 6, 2 ( 2) = 3 6 2 Magnitude of ( 2) = (32+( 6)2+( 2)2) |( 2) |= (9+36+4) = 49 = 7 So, cos = |((2 " " + 1 " " 2 ) . (3 " " 6 " " 2 ))/(3 7)| = |((2 3) + (1 6) + ( 2 2))/21| = |(6 6 + 4)/21| = 4/21 So, cos = 4/21 = cos-1( / ) Therefore, two angle between the two planes is cos-1(4/21)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.