Ex 10.2, 10 - Chapter 10 Class 12 Vector Algebra (Important Question)

Last updated at Dec. 16, 2024 by Teachoo

Find a vector in direction of vector 5i -j + 2k which has magnitude 8

Ex 10.2, 10 - Chapter 10 Class 12 Vector Algebra - Part 2

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Transcript

Ex 10.2, 10 Find a vector in the direction of vector 5𝑖 ̂ − 𝑗 ̂ + 2𝑘 ̂ which has magnitude 8 units.𝑎 ⃗ = 5𝑖 ̂ − 𝑗 ̂ + 2𝑘 ̂ = 5𝑖 ̂ − 1𝑗 ̂ + 2𝑘 ̂ Magnitude of 𝑎 ⃗ = √(52+(−1)2+22) |𝑎 ⃗ | = √(25+1+4) = √30 Unit vector in direction of 𝑎 ⃗ = 1/|𝑎 ⃗ | . 𝑎 ⃗ 𝑎 ̂ = 1/√30 . [5𝑖 ̂−1𝑗 ̂+2𝑘 ̂ ] 𝑎 ̂ = 5/√30 𝑖 ̂ − 1/√30 𝑗 ̂ + 2/√30 𝑘 ̂ Thus, unit vector 𝑎 ̂ = 5/√30 𝑖 ̂ − 1/√30 𝑗 ̂ + 2/√30 𝑘 ̂ Vector with magnitude 1 = 5/√30 𝑖 ̂ − 1/√30 𝑗 ̂ + 2/√30 𝑘 ̂ Vector with magnitude 8 = 8 [5/√30 𝑖 ̂" − " 1/√30 𝑗 ̂" + " 2/√30 𝑘 ̂ ] = 𝟒𝟎/√𝟑𝟎 𝒊 ̂ – 𝟖/√𝟑𝟎 𝒋 ̂ + 𝟏𝟔/√𝟑𝟎 𝒌 ̂ Hence, the required vector is 40/√30 𝑖 ̂ – 8/√30 𝑗 ̂ + 16/√30 𝑘 ̂

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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

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