Last updated at May 29, 2018 by Teachoo

Transcript

Misc 23 (Method 1) The planes: 2x y + 4z = 5 and 5x 2.5y + 10z = 6 are (A) Perpendicular (B) Parallel (C) intersect y-axis (D) passes through 0,0, 5 4 Angle between two planes A1x + B1y + C1z = d1 and A2x + B2y + C2z = d2 is given by cos = + + + + + + Given the two planes are So, cos = 2 10 + 1 5 + (4 20) 2 2 + ( 1) 2 + 4 2 10 2 + ( 5) 2 + 20 2 = 20 + 5 + 80 4 + 1 + 16 100 + 25 + 400 = 105 21 525 = 105 21 25 21 = 105 21 5 21 = 105 21 5 = 1 So, cos = 1 = 0 Since angle between the planes is 0 , Therefore, the planes are parallel. So, option (B) is correct Misc 23 (Method 2) The planes: 2x y + 4z = 5 and 5x 2.5y + 10z = 6 are (A) Perpendicular (B) Parallel (C) intersect y-axis (D) passes through 0,0, 5 4 Given, two planes are Two lines are parallel if their direction ratios are proportional. 1 2 = 2 10 = 1 5 , 1 2 = 1 5 = 1 5 , 1 2 = 4 20 = 1 5 Since, = = = , Therefore, the normal vectors of the two planes are parallel. So, the two planes are parallel. So, option (B) is correct

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.