Get live Maths 1-on-1 Classs - Class 6 to 12

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 Important

Example 11

Example 12 Important

Example 13 Important Deleted for CBSE Board 2023 Exams

Example 14 Deleted for CBSE Board 2023 Exams

Example 15 Deleted for CBSE Board 2023 Exams

Example 16 Important Deleted for CBSE Board 2023 Exams

Example 17 Deleted for CBSE Board 2023 Exams

Example 18 Deleted for CBSE Board 2023 Exams

Example 19 Important Deleted for CBSE Board 2023 Exams

Example 20 Important Deleted for CBSE Board 2023 Exams

Example 21 Important Deleted for CBSE Board 2023 Exams

Example 22 Deleted for CBSE Board 2023 Exams

Example 23 Important Deleted for CBSE Board 2023 Exams

Example 24 Deleted for CBSE Board 2023 Exams

Example, 25 Important Deleted for CBSE Board 2023 Exams You are here

Example 26

Example 27 Important Deleted for CBSE Board 2023 Exams

Example 28 Important Deleted for CBSE Board 2023 Exams

Example 29 Important

Example 30 Important Deleted for CBSE Board 2023 Exams

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

Last updated at March 16, 2023 by Teachoo

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).