Ex 10.2, 15 - Find position vector of a point R divides line - Ex 10.2

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.2, 15 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ and โ€“ ๐‘–๏ทฏ + ๐‘—๏ทฏ + ๐‘˜๏ทฏ respectively, in the ratio 2 : 1 (i) internally ๐‘‚๐‘ƒ๏ทฏ= ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ ๐‘‚๐‘„๏ทฏ= โ€“ ๐‘–๏ทฏ + ๐‘—๏ทฏ + ๐‘˜๏ทฏ Position vector of R = 2. ๐‘‚๐‘„๏ทฏ + 1. ๐‘‚๐‘ƒ๏ทฏ๏ทฎ2 + 1๏ทฏ ๐‘‚๐‘…๏ทฏ = 2 โˆ’ ๐‘–๏ทฏ + ๐‘—๏ทฏ + ๐‘˜๏ทฏ๏ทฏ + 1( ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + ๐‘˜๏ทฏ)๏ทฎ3๏ทฏ = โˆ’2 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 2 ๐‘˜๏ทฏ + ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ๏ทฎ3๏ทฏ = โˆ’ ๐‘–๏ทฏ + 4 ๐‘—๏ทฏ + ๐‘˜๏ทฏ๏ทฎ3๏ทฏ Thus, position vector of R dividing P and Q internally is โˆ’๐Ÿ๏ทฎ๐Ÿ‘๏ทฏ ๐’Š๏ทฏ + ๐Ÿ’๏ทฎ๐Ÿ‘๏ทฏ ๐’Š๏ทฏ + ๐Ÿ๏ทฎ๐Ÿ‘๏ทฏ ๐’Œ๏ทฏ Ex 10.2, 15 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ and โ€“ ๐‘–๏ทฏ + ๐‘—๏ทฏ + ๐‘˜๏ทฏ respectively, in the ratio 2 : 1 (ii) externally Position vector of R = 2 ๐‘‚๐‘„๏ทฏ โˆ’ 1 ๐‘‚๐‘ƒ๏ทฏ๏ทฎ2 โˆ’ 1๏ทฏ ๐‘‚๐‘…๏ทฏ = 2 โˆ’ ๐‘–๏ทฏ + ๐‘—๏ทฏ + ๐‘˜๏ทฏ๏ทฏโˆ’1( ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ โˆ’ ๐‘˜๏ทฏ)๏ทฎ2โˆ’1๏ทฏ ๐‘‚๐‘…๏ทฏ = โˆ’2 ๐‘–๏ทฏ + 2 ๐‘—๏ทฏ + 2 ๐‘˜๏ทฏ โˆ’ ๐‘–๏ทฏ โˆ’ 2 ๐‘—๏ทฏ + ๐‘˜๏ทฏ๏ทฎ2โˆ’1๏ทฏ ๐‘‚๐‘…๏ทฏ = โ€“3 ๐’Š๏ทฏ + 3 ๐’Œ๏ทฏ Thus, position vector of R dividing P and Q externally is โˆ’3 ๐‘–๏ทฏ + 3 ๐‘˜๏ทฏ

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