Example 7 - Chapter 10 Class 12 Vector Algebra
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 7 Find a vector in the direction of vector 𝑎 ⃗ = 𝑖 ̂ − 2𝑗 ̂ that has magnitude 7 units. Given 𝒂 ⃗ = 𝑖 ̂ – 2𝑗 ̂ = 1𝑖 ̂ – 2𝑗 ̂ + 0𝑘 ̂ Magnitude of 𝒂 ⃗ = √(12+(−2)2+02) |𝒂 ⃗ | = √(1+4+0) = √𝟓 Unit vector in direction of 𝑎 ⃗ = 𝟏/(𝑴𝒂𝒈𝒏𝒊𝒕𝒖𝒅𝒆 𝒐𝒇 𝒂 ⃗ ) × 𝒂 ⃗ 𝑎 ̂ = 1/√5 ["1" 𝑖 ̂" + " 2𝑗 ̂" + " 0𝑘 ̂ ] 𝑎 ̂ = 1/√5 𝑖 ̂ − 2/√5 𝑗 ̂ Thus, Vector having a magnitude 1 = 1/√5 𝑖 ̂ − 2/√5 𝑗 ̂ Vector having a magnitude 7 = 7[1/√5 " " 𝑖 ̂" − " 2/√5 " " 𝑗 ̂" " ] = 7/√5 " " 𝑖 ̂" − " 14/√5 " " 𝑗 ̂ Thus, required vector is 𝟕/√𝟓 " " 𝒊 ̂" − " 𝟏𝟒/√𝟓 " " 𝒋 ̂
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo