Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg
Example, 25 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at Feb. 1, 2020 by Teachoo
Transcript
Example, 25 Find the angle between the line (π₯ + 1)/2 = π¦/3 = (π§ β 3)/6 And the plane 10x + 2y β 11z = 3. The angle between a line (π₯ β π₯_1)/π = (π¦ β π¦_1)/π = (π§ βγ π§γ_1)/π and the normal to the plane Ax + By + Cz = D is given by cos ΞΈ = |(π΄π + π΅π + πΆπ)/(β(π^2 + π^2 +γ πγ^2 ) β(π΄^2 +γ π΅γ^2 +γ πΆγ^2 ))| So, angle between line and plane is given by sin π = |(π΄π + π΅π + πΆπ)/(β(π^2 + π^2 + π^2 )+β(π΄^2 + π΅^2 +γ πΆγ^2 ))| Given, the line is (π₯ + 1)/2 = π¦/3 = (π§ β 3)/6 (π₯ β (β1))/2 = (π¦ β 0)/3 = (π§ β 3)/6 Comparing with (π₯ βγ π₯γ_1)/π = (π¦ β π¦_1)/π = (π§ β π§_1)/π , π = 2, b = 3, c = 6 The plane is 10x + 2y β 11z = 3 Comparing with Ax + By + Cz = D, A = 10, B = 2, C = β11 So, sin Ο = |((10 Γ 2) + (2 Γ 3) + (β11 Γ 6))/(β(2^2 + 3^2 + 6^2 ) β(γ10γ^(2 )+γ 2γ^2 + γ(β11)γ^2 ))| = |(20 + 6 β 66)/(β(4 + 9 + 36) β(100 + 4 + 121))| = |(β40)/(7 Γ 15)| = 8/21 So, sin Ο = 8/21 β΄ π = γπππγ^(βπ)β‘(π/ππ) Therefore, the angle between the given line and plane is sin^(β1)β‘(8/21).
Examples
Example 1
Example, 2 Important
Example, 3
Example, 4 Important
Example, 5 Important
Example, 6 Important
Example, 7
Example 8
Example, 9
Example 10
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
Example 23 Important
Example 24
Example, 25 Important You are here
Example 26
Example 27 Important
Example 28 Important
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.