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Example 7 - Find a vector in direction of vector a = i - 2j

Example 7 - Chapter 10 Class 12 Vector Algebra - Part 2

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Transcript

Example 7 Find a vector in the direction of vector π‘Ž βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ that has magnitude 7 units. Given 𝒂 βƒ— = 𝑖 Μ‚ – 2𝑗 Μ‚ = 1𝑖 Μ‚ – 2𝑗 Μ‚ + 0π‘˜ Μ‚ Magnitude of 𝒂 βƒ— = √(12+(βˆ’2)2+02) |𝒂 βƒ— | = √(1+4+0) = βˆšπŸ“ Unit vector in direction of π‘Ž βƒ— = 𝟏/(π‘΄π’‚π’ˆπ’π’Šπ’•π’–π’…π’† 𝒐𝒇 𝒂 βƒ— ) Γ— 𝒂 βƒ— π‘Ž Μ‚ = 1/√5 ["1" 𝑖 Μ‚" + " 2𝑗 Μ‚" + " 0π‘˜ Μ‚ ] π‘Ž Μ‚ = 1/√5 𝑖 Μ‚ βˆ’ 2/√5 𝑗 Μ‚ Thus, Vector having a magnitude 1 = 1/√5 𝑖 Μ‚ βˆ’ 2/√5 𝑗 Μ‚ Vector having a magnitude 7 = 7[1/√5 " " 𝑖 Μ‚" βˆ’ " 2/√5 " " 𝑗 Μ‚" " ] = 7/√5 " " 𝑖 Μ‚" βˆ’ " 14/√5 " " 𝑗 Μ‚ Thus, required vector is πŸ•/βˆšπŸ“ " " π’Š Μ‚" βˆ’ " πŸπŸ’/βˆšπŸ“ " " 𝒋 Μ‚

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.