Example 22 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at May 29, 2018 by Teachoo
Transcript
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)
Examples
Example 1
Example, 2
Example, 3 Important
Example, 4
Example, 5
Example, 6 Important
Example, 7
Example 8
Example, 9 Important
Example 10
Example 11
Example 12 Important
Example 13
Example 14
Example 15
Example 16
Example 17
Example 18
Example 19
Example 20 Important
Example 21 Important
Example 22 You are here
Example 23 Important
Example 24 Important
Example, 25 Important
Example 26
Example 27 Important
Example 28
Example 29 Important
Example 30 Important
Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.