Check sibling questions

Ex 11.3

Ex 11.3, 1 (a) Deleted for CBSE Board 2023 Exams

Ex 11.3, 1 (b) Deleted for CBSE Board 2023 Exams

Ex 11.3, 1 (c) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 1 (d) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 2 Deleted for CBSE Board 2023 Exams

Ex 11.3, 3 (a) Deleted for CBSE Board 2023 Exams

Ex 11.3, 3 (b) Deleted for CBSE Board 2023 Exams

Ex 11.3, 3 (c) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 4 (a) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 4 (b) Deleted for CBSE Board 2023 Exams

Ex 11.3, 4 (c) Deleted for CBSE Board 2023 Exams

Ex 11.3, 4 (d) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 5 (a) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 5 (b) Deleted for CBSE Board 2023 Exams

Ex 11.3, 6 (a) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 6 (b) Deleted for CBSE Board 2023 Exams

Ex 11.3, 7 Deleted for CBSE Board 2023 Exams

Ex 11.3, 8 Deleted for CBSE Board 2023 Exams

Ex 11.3, 9 Deleted for CBSE Board 2023 Exams

Ex 11.3, 10 Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 11 Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 12 Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 13 (a) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 13 (b) Important Deleted for CBSE Board 2023 Exams You are here

Ex 11.3, 13 (c) Deleted for CBSE Board 2023 Exams

Ex 11.3, 13 (d) Deleted for CBSE Board 2023 Exams

Ex 11.3, 13 (e) Deleted for CBSE Board 2023 Exams

Ex 11.3, 14 (a) Important Deleted for CBSE Board 2023 Exams

Ex 11.3, 14 (b) Deleted for CBSE Board 2023 Exams

Ex 11.3, 14 (c) Deleted for CBSE Board 2023 Exams

Ex 11.3, 14 (d) Important Deleted for CBSE Board 2023 Exams

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

Ex 11.3, 13 (b) - Find angle b/w planes 2x+y+3z-2=0 and x - 2y + 5 = 0

Ex 11.3, 13 (b) - Chapter 11 Class 12 Three Dimensional Geometry - Part 2
Ex 11.3, 13 (b) - Chapter 11 Class 12 Three Dimensional Geometry - Part 3

Β 

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


Transcript

Ex 11.3, 13 In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. (b) 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0 Check parallel Two lines with direction ratios 𝐴_1, 𝐡_1, 𝐢_1 and 𝐴_2, 𝐡_2, 𝐢_2 are parallel if 𝑨_𝟏/𝑨_𝟐 = 𝑩_𝟏/𝑩_𝟐 = π‘ͺ_𝟏/π‘ͺ_𝟐 So, 𝐴_1/𝐴_2 = 2/(βˆ’1) = βˆ’2, 𝐡_1/𝐡_2 = 1/2 , 𝐢_1/𝐢_2 = 3/0 Since, direction ratios are not proportional, the two normal are not parallel. ∴ Given two planes are not parallel. Check perpendicular Two lines with direction ratios 𝐴_1, 𝐡_1, 𝐢_1 and 𝐴_2, 𝐡_2, 𝐢_2 are perpendicular if 𝑨_𝟏 𝑨_𝟐 + 𝑩_𝟏 𝑩_𝟐 + π‘ͺ_𝟏 π‘ͺ_𝟐 = 0 Now, 𝐴_1 𝐴_2 + 𝐡_1 𝐡_2 + 𝐢_1 𝐢_2 = (2 Γ— βˆ’1) + (1 Γ— 2) + (3 Γ— 0) = βˆ’2 + 2 + 0 = 0 Since 𝐴_1 𝐴_2 + 𝐡_1 𝐡_2 + 𝐢_1 𝐢_2 = 0 The two normal are perpendicular. Since normal are perpendicular, planes are perpendicular.

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.