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Misc 9 - Find R, if it divides P(2a + b), Q(a - 3b) externally

Misc 9 - Chapter 10 Class 12 Vector Algebra - Part 2
Misc 9 - Chapter 10 Class 12 Vector Algebra - Part 3

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Misc 9 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2π‘Ž βƒ— + 𝑏 βƒ—) and (π‘Ž βƒ— – 3𝑏 βƒ—) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ. Given (𝑂𝑃) βƒ— = 2π‘Ž βƒ— + 𝑏 βƒ— (𝑂𝑄) βƒ— = π‘Ž βƒ— βˆ’ 3𝑏 βƒ— Since R divides PQ externally in the ratio 1 : 2 Position vector of R = (𝟏 Γ— (𝑢𝑸) βƒ— βˆ’ 𝟐 Γ— (𝑢𝑷) βƒ—)/(𝟏 βˆ’ 𝟐) (𝑂𝑅) βƒ— = (1(π‘Ž βƒ— βˆ’ 3𝑏 βƒ— ) βˆ’ 2(2π‘Ž βƒ— + 𝑏 βƒ—))/(βˆ’1) = (π‘Ž βƒ— βˆ’ 3𝑏 βƒ— βˆ’ 4π‘Ž βƒ— βˆ’ 2𝑏 βƒ—)/(βˆ’1) = (βˆ’3π‘Ž βƒ— βˆ’ 5𝑏 βƒ— )/(βˆ’1) = πŸ‘π’‚ βƒ—+πŸ“π’ƒ βƒ— Thus, position vector of R = (𝑂𝑅) βƒ— = 3π‘Ž βƒ—+5𝑏 βƒ— Finding mid point of RQ Position vector of mid-point = ((𝑂𝑄) βƒ— + (𝑂𝑅) βƒ—)/2 = (π‘Ž βƒ— βˆ’ 3𝑏 βƒ— + 3π‘Ž βƒ— + 5𝑏 βƒ—)/2 = (4π‘Ž βƒ— + 2𝑏 βƒ—)/2 = 2π‘Ž βƒ—+𝑏 βƒ— This is the position vector of P. Thus, P is the mid point of RQ. Hence proved

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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.