Example 11 - Given P & Q with position vector OP = 3a - 2b, OQ = a + b

Example 11 - Chapter 10 Class 12 Vector Algebra - Part 2

Example 11 - Chapter 10 Class 12 Vector Algebra - Part 3

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

Transcript

Example 11 Consider two points P and Q with position vectors (𝑂𝑃) βƒ— = 3π‘Ž βƒ— βˆ’ 2𝑏 βƒ— and (𝑂𝑄) βƒ— = π‘Ž βƒ— + 𝑏 βƒ— . Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (i) internally, and Given (𝑂𝑃) βƒ— = 3π‘Ž βƒ— βˆ’ 2𝑏 βƒ— (𝑂𝑄) βƒ— = π‘Ž βƒ— + 𝑏 βƒ— Position vector of R = (𝟐(𝑢𝑸) βƒ— + 𝟏(𝑢𝑷) βƒ—)/(𝟐 + 𝟏) (𝑂𝑅) βƒ— = (2(π‘Ž βƒ— + 𝑏 βƒ— ) + 1(3π‘Ž βƒ— βˆ’ 2𝑏 βƒ— ))/(2 + 1) = (2π‘Ž βƒ— + 2𝑏 βƒ— + 3π‘Ž βƒ— βˆ’ 2𝑏 βƒ—)/3 = (πŸ“π’‚ βƒ—)/πŸ‘ Thus, position vector of R dividing P and Q internally is (5π‘Ž βƒ—)/3. Example 11 Consider two points P and Q with position vectors (𝑂𝑃) βƒ— = 3π‘Ž βƒ— βˆ’ 2𝑏 βƒ— and (𝑂𝑄) βƒ— = π‘Ž βƒ— + 𝑏 βƒ— . Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (ii) externally. Position vector of R = (2(𝑂𝑄) βƒ— βˆ’ 1(𝑂𝑃) βƒ—)/(𝟐 βˆ’ 𝟏) (𝑂𝑅) βƒ— = (2(π‘Ž βƒ— + 𝑏 βƒ— ) βˆ’ 1(3π‘Ž βƒ— βˆ’ 2𝑏 βƒ—))/(2 βˆ’ 1) = (2π‘Ž βƒ— + 2𝑏 βƒ— βˆ’ 3π‘Ž βƒ— + 2𝑏 βƒ—)/1 = βˆ’π‘Ž βƒ— + 4𝑏 βƒ— = 4𝒃 βƒ— βˆ’ 𝒂 βƒ—

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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.