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 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.

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.