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Ex 10.2, 15 - Find position vector of a point R divides line

Ex 10.2, 15 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.2, 15 - Chapter 10 Class 12 Vector Algebra - Part 3


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Ex 10.2, 15 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 𝑖 ̂ + 2𝑗 ̂ − 𝑘 ̂ and – 𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂ respectively, in the ratio 2 : 1 (i) internally (𝑂𝑃) ⃗= 𝑖 ̂ + 2𝑗 ̂ − 𝑘 ̂ (𝑂𝑄) ⃗= – 𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂ Position vector of R = (2.(𝑂𝑄) ⃗ + 1.(𝑂𝑃) ⃗)/(2 + 1) (𝑂𝑅) ⃗ = (2(−𝑖 ̂" + " 𝑗 ̂" + " 𝑘 ̂ ) + 1(𝑖 ̂" +" 2𝑗 ̂" + " 𝑘 ̂))/3 = (−2𝑖 ̂ + 2𝑗 ̂ + 2𝑘 ̂ + 𝑖 ̂ + 2𝑗 ̂ −( 𝑘) ̂)/3 = (−𝑖 ̂ + 4𝑗 ̂ + 𝑘 ̂)/3 Thus, position vector of R dividing P and Q internally is (−𝟏)/𝟑 𝒊 ̂ + 𝟒/𝟑 𝒊 ̂ + 𝟏/𝟑 𝒌 ̂ Ex 10.2, 15 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 𝑖 ̂ + 2 𝑗 ̂ − 𝑘 ̂ and – 𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂ respectively, in the ratio 2 : 1 (ii) externally Position vector of R = (2(𝑂𝑄) ⃗ − 1(𝑂𝑃) ⃗)/(2 − 1) (𝑂𝑅) ⃗ = (2(−𝑖 ̂" + " 𝑗 ̂" + " 𝑘 ̂ )−1(𝑖 ̂" + " 2𝑗 ̂" − " 𝑘 ̂))/(2−1) (𝑂𝑅) ⃗ = (−2𝑖 ̂ + 2𝑗 ̂ + 2𝑘 ̂ − 𝑖 ̂ − 2𝑗 ̂ + 𝑘 ̂)/(2−1) (𝑂𝑅) ⃗ = –3𝒊 ̂ + 3𝒌 ̂ Thus, Position vector of R dividing P and Q externally is −3𝑖 ̂ + 3𝑘 ̂

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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.