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

  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.