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

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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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