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Misc 4 - If a = b + c, then is it true that |a| = |b| + |c|

Misc 4 - Chapter 10 Class 12 Vector Algebra - Part 2
Misc 4 - Chapter 10 Class 12 Vector Algebra - Part 3

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Misc 4 If π‘Ž βƒ— = 𝑏 βƒ— + 𝑐 βƒ— , then is it true that |π‘Ž βƒ—|=|𝑏 βƒ—| + |𝑐 βƒ—| Justify your answer.Given, 𝒂 βƒ— = 𝒃 βƒ— + 𝒄 βƒ— Let 𝒃 βƒ— = 1𝑖 Μ‚ + 2𝑗 Μ‚ + 3π‘˜ Μ‚ & 𝒄 βƒ— = 2𝑖 Μ‚ βˆ’ 1𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Thus, 𝒂 βƒ— = (𝑏 βƒ— + 𝑐 βƒ—) = (1 + 2) 𝑖 Μ‚ + (2 βˆ’ 1) 𝑗 Μ‚ + (3 βˆ’ 2) π‘˜ Μ‚ = 3π’Š Μ‚ + 1𝒋 Μ‚ + 1π’Œ Μ‚ Given, 𝒂 βƒ— = 𝒃 βƒ— + 𝒄 βƒ— Let 𝒃 βƒ— = 1𝑖 Μ‚ + 2𝑗 Μ‚ + 3π‘˜ Μ‚ & 𝒄 βƒ— = 2𝑖 Μ‚ βˆ’ 1𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Thus, 𝒂 βƒ— = (𝑏 βƒ— + 𝑐 βƒ—) = (1 + 2) 𝑖 Μ‚ + (2 βˆ’ 1) 𝑗 Μ‚ + (3 βˆ’ 2) π‘˜ Μ‚ = 3π’Š Μ‚ + 1𝒋 Μ‚ + 1π’Œ Μ‚ Given, 𝒂 βƒ— = 𝒃 βƒ— + 𝒄 βƒ— Let 𝒃 βƒ— = 1𝑖 Μ‚ + 2𝑗 Μ‚ + 3π‘˜ Μ‚ & 𝒄 βƒ— = 2𝑖 Μ‚ βˆ’ 1𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Thus, 𝒂 βƒ— = (𝑏 βƒ— + 𝑐 βƒ—) = (1 + 2) 𝑖 Μ‚ + (2 βˆ’ 1) 𝑗 Μ‚ + (3 βˆ’ 2) π‘˜ Μ‚ = 3π’Š Μ‚ + 1𝒋 Μ‚ + 1π’Œ Μ‚ Finding |𝒂 βƒ— |, |𝒃 βƒ— | , |𝒄 βƒ— | Magnitude of π‘Ž βƒ— = √(32+1^2+1^2 ) |𝒂 βƒ— | = √(9+1+1) = √𝟏𝟏 Magnitude of 𝑏 βƒ— = √(12+22+32) |𝒃 βƒ— | = √(1+4+9) = βˆšπŸπŸ’ Magnitude of 𝑐 βƒ— = √(22+(βˆ’1)2+(βˆ’2)2) |𝒄 βƒ— | = √(4+1+4) = √9 = 3 Now, |𝒃 βƒ— | + |𝒄 βƒ— | = √14 + 3 β‰  √11 β‰  |𝒂 βƒ— | So, |π‘Ž βƒ— |β‰  |𝑏 βƒ— | + |𝑐 βƒ— | Hence, the given statement is False.

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Davneet Singh

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.