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

Transcript

Example 11 Consider two points P and Q with position vectors (๐‘‚๐‘ƒ) โƒ— = 3๐‘Ž โƒ— โˆ’ 2๐‘ โƒ— and (๐‘‚๐‘„) โƒ— = ๐‘Ž โƒ— + ๐‘ โƒ— . 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) โƒ— = 3๐‘Ž โƒ— โˆ’ 2๐‘ โƒ— (๐‘‚๐‘„) โƒ— = ๐‘Ž โƒ— + ๐‘ โƒ— Position vector of R = (2(๐‘‚๐‘„) โƒ— + 1(๐‘‚๐‘ƒ) โƒ—)/(2 + 1) (๐‘‚๐‘…) โƒ— = (2(๐‘Ž โƒ— + ๐‘ โƒ— ) + 1(3๐‘Ž โƒ— โˆ’ 2๐‘ โƒ— ))/(2 + 1) = (2๐‘Ž โƒ— + 2๐‘ โƒ— + 3๐‘Ž โƒ— โˆ’ 2๐‘ โƒ—)/3 ] Thus, position vector of R dividing P and Q internally is (5๐‘Ž โƒ—)/3. Example 11 Consider two points P and Q with position vectors (๐‘‚๐‘ƒ) โƒ— = 3๐‘Ž โƒ— โˆ’ 2๐‘ โƒ— and (๐‘‚๐‘„) โƒ— = ๐‘Ž โƒ— + ๐‘ โƒ— . 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‘„) โƒ— โˆ’ 1(๐‘‚๐‘ƒ) โƒ—)/(๐Ÿ โˆ’ ๐Ÿ) (๐‘‚๐‘…) โƒ— = (2(๐‘Ž โƒ— + ๐‘ โƒ— ) โˆ’ 1(3๐‘Ž โƒ— โˆ’ 2๐‘ โƒ—))/(2 โˆ’ 1) = (2๐‘Ž โƒ— + 2๐‘ โƒ— โˆ’ 3๐‘Ž โƒ— + 2๐‘ โƒ—)/1 = โˆ’๐‘Ž โƒ— + 4๐‘ โƒ— = 4๐’ƒ โƒ— โˆ’ ๐’‚ โƒ— Thus, position vector of R dividing P and Q externally is 4๐‘ โƒ— โ€“ ๐‘Ž โƒ—

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.