Check sibling questions

Ex 10.4, 9 - Find area of triangle A(1, 1, 2), B(2, 3, 5)

Ex 10.4, 9 - Chapter 10 Class 12 Vector Algebra - Part 2

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Transcript

Ex 10.4, 9 Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5). A (1, 1, 2) , B (2, 3, 5) , C (1, 5, 5) Area of triangle ABC is 1/2 |(𝐴𝐡) βƒ— Γ— (𝐴𝐢) βƒ— | A (1, 1, 2) B (2, 3, 5) (𝐴𝐡) βƒ— = (2 βˆ’ 1) 𝑖 Μ‚ + (3 βˆ’ 1) 𝑗 Μ‚ + (5 βˆ’ 2) π‘˜ Μ‚ = 1𝑖 Μ‚ + 2𝑗 Μ‚ + 3π‘˜ Μ‚ A (1, 1, 2) C (1, 5, 5) (𝐴𝐢) βƒ— = (1 βˆ’ 1) 𝑖 Μ‚ + (5 βˆ’ 1) 𝑗 Μ‚ + (5 βˆ’ 2) π‘˜ Μ‚ = 0𝑖 Μ‚ + 4𝑗 Μ‚ + 3π‘˜ Μ‚ (𝑨𝑩) βƒ— Γ— (𝑨π‘ͺ) βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@1&2&3@0&4&3)| = 𝑖 Μ‚ (2Γ—3βˆ’4Γ—3 )βˆ’π‘— Μ‚ (1Γ—3βˆ’0Γ—3 )+π‘˜ Μ‚ (1Γ—4βˆ’0Γ—2 ) = 𝑖 Μ‚ (6βˆ’12)βˆ’π‘— Μ‚(3βˆ’0) + π‘˜ Μ‚ (4βˆ’0) = βˆ’6π’Š Μ‚ – 3𝒋 Μ‚ + 4π’Œ Μ‚ Magnitude of (𝐴𝐡) βƒ— Γ— (𝐴𝐢) βƒ— = √((βˆ’6)2+(βˆ’3)2+42) |(𝐴𝐡) βƒ—" Γ— " (𝐴𝐢) βƒ— | = √(36+9+16) = √61 Area of triangle ABC = 1/2 |(𝐴𝐡) βƒ—" Γ— " (𝐴𝐢) βƒ— | = 1/2 Γ— √61 = βˆšπŸ”πŸ/𝟐

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.