Check sibling questions

Show that points A (1, 2, 7), B (2, 6, 3), C (3, 10, -1) are collinear

Ex 10.3, 16 - Chapter 10 Class 12 Vector Algebra - Part 2

Ex 10.3, 16 - Chapter 10 Class 12 Vector Algebra - Part 3 Ex 10.3, 16 - Chapter 10 Class 12 Vector Algebra - Part 4

 


Transcript

Ex 10.3, 16 (Introduction) Show that the points A (1, 2, 7), B (2, 6, 3) & C (3, 10, –1) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three vectors collinear i.e. |(𝐴𝐵) ⃗ | + |(𝐵𝐶) ⃗ | = |(𝐴𝐶) ⃗ | (𝐵𝐶) ⃗ = (3 − 2) 𝑖 ̂ + (10 − 6) 𝑗 ̂ + (−1 − 3) 𝑘 ̂ = 1𝑖 ̂ + 4𝑗 ̂ − 4𝑘 ̂ (𝐴𝐶) ⃗ = (3 − 1) 𝑖 ̂ + (10 − 2) 𝑗 ̂ + (−1 − 7) 𝑘 ̂ = 2𝑖 ̂ + 8𝑗 ̂ − 8𝑘 ̂ Magnitude of (𝐴𝐵) ⃗ = √(12+42+(−4)2) |(𝐴𝐵) ⃗ | = √(1+16+16) = √33 Magnitude of (𝐵𝐶) ⃗ = √(12+42+(−4)2) |(𝐵𝐶) ⃗ | = √(1+16+16) = √33 Magnitude of (𝐴𝐶) ⃗ = √(22+82+(−8)2) |(𝐵𝐶) ⃗ | = √(4+64+64) = √132 = √(4×33 ) = 2√(33 ) Thus, |(𝐴𝐵) ⃗ | + |(𝐵𝐶) ⃗ | = √(33 ) + √(33 ) = 2√(33 ) = |(𝐴𝐶) ⃗ | Thus, A, B and C are collinear.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.