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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


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 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.