Example 11 - OP = 3a - 2b, OQ = a + b. Find position vector - Examples

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 11 Consider two points P and Q with position vectors ๐‘‚๐‘ƒ๏ทฏ = 3 ๐‘Ž๏ทฏ โˆ’ 2 ๐‘๏ทฏ and ๐‘‚๐‘„๏ทฏ = ๐‘Ž๏ทฏ + ๐‘๏ทฏ . Find the position vector of a point R which divides the line joining P and Q in the ratio 2 : 1, (i) internally, and ๐‘‚๐‘ƒ๏ทฏ = 3 ๐‘Ž๏ทฏ โˆ’ 2 ๐‘๏ทฏ ๐‘‚๐‘„๏ทฏ = ๐‘Ž๏ทฏ + ๐‘๏ทฏ Position vector of R = 2 ๐‘‚๐‘„๏ทฏ + 1 ๐‘‚๐‘ƒ๏ทฏ๏ทฎ2 + 1๏ทฏ ๐‘‚๐‘…๏ทฏ = 2 ๐‘Ž๏ทฏ + ๐‘๏ทฏ๏ทฏ + 1 3 ๐‘Ž๏ทฏ โˆ’ 2 ๐‘๏ทฏ๏ทฏ๏ทฎ2 + 1๏ทฏ = 2 ๐‘Ž๏ทฏ + 2 ๐‘๏ทฏ + 3 ๐‘Ž๏ทฏ โˆ’ 2 ๐‘๏ทฏ๏ทฎ3๏ทฏ = ๐Ÿ“ ๐’‚๏ทฏ๏ทฎ๐Ÿ‘๏ทฏ Thus, position vector of R dividing P and Q internally is 5 ๐‘Ž๏ทฏ๏ทฎ3๏ทฏ. Example 11 Consider two points P and Q with position vectors ๐‘‚๐‘ƒ๏ทฏ = 3 ๐‘Ž๏ทฏ โˆ’ 2 ๐‘๏ทฏ and ๐‘‚๐‘„๏ทฏ = ๐‘Ž๏ทฏ + ๐‘๏ทฏ . 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 ๐‘‚๐‘„๏ทฏ โˆ’ 1 ๐‘‚๐‘ƒ๏ทฏ๏ทฎ๐Ÿ โˆ’ ๐Ÿ๏ทฏ ๐‘‚๐‘…๏ทฏ = 2 ๐‘Ž๏ทฏ + ๐‘๏ทฏ๏ทฏ โˆ’ 1(3 ๐‘Ž๏ทฏ โˆ’ 2 ๐‘๏ทฏ)๏ทฎ2โˆ’1๏ทฏ = 2 ๐‘Ž๏ทฏ + 2 ๐‘๏ทฏ โˆ’ 3 ๐‘Ž๏ทฏ + 2 ๐‘๏ทฏ๏ทฎ1๏ทฏ = โˆ’ ๐‘Ž๏ทฏ + 4 ๐‘๏ทฏ = 4 ๐’ƒ๏ทฏ โˆ’ ๐’‚๏ทฏ Thus, position vector of R dividing P and Q externally is 4 ๐‘๏ทฏ โ€“ ๐‘Ž๏ทฏ

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