
Examples
Example, 2 Important
Example, 3
Example, 4 Important
Example, 5 Important
Example, 6 Important
Example, 7
Example 8
Example, 9 Deleted for CBSE Board 2022 Exams
Example 10 Important Deleted for CBSE Board 2022 Exams
Example 11
Example 12 Important
Example 13 Important
Example 14
Example 15
Example 16 Important
Example 17
Example 18
Example 19 Important
Example 20 Important
Example 21 Important
Example 22 Deleted for CBSE Board 2022 Exams You are here
Example 23 Important Deleted for CBSE Board 2022 Exams
Example 24
Example, 25 Important Deleted for CBSE Board 2022 Exams
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Example 30 Important
Last updated at May 29, 2018 by Teachoo
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)