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

Transcript

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‘– ฬ‚ + 2๐‘— ฬ‚ โˆ’ ๐‘˜ ฬ‚ and โ€“ ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ respectively, in the ratio 2 : 1 (i) internally (๐‘‚๐‘ƒ) โƒ—= ๐‘– ฬ‚ + 2๐‘— ฬ‚ โˆ’ ๐‘˜ ฬ‚ (๐‘‚๐‘„) โƒ—= โ€“ ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ Position vector of R = (2.(๐‘‚๐‘„) โƒ— + 1.(๐‘‚๐‘ƒ) โƒ—)/(2 + 1) (๐‘‚๐‘…) โƒ— = (2(โˆ’๐‘– ฬ‚" + " ๐‘— ฬ‚" + " ๐‘˜ ฬ‚ ) + 1(๐‘– ฬ‚" +" 2๐‘— ฬ‚" + " ๐‘˜ ฬ‚))/3 = (โˆ’2๐‘– ฬ‚ + 2๐‘— ฬ‚ + 2๐‘˜ ฬ‚ + ๐‘– ฬ‚ + 2๐‘— ฬ‚ โˆ’( ๐‘˜) ฬ‚)/3 = (โˆ’๐‘– ฬ‚ + 4๐‘— ฬ‚ + ๐‘˜ ฬ‚)/3 Thus, position vector of R dividing P and Q internally is (โˆ’๐Ÿ)/๐Ÿ‘ ๐’Š ฬ‚ + ๐Ÿ’/๐Ÿ‘ ๐’Š ฬ‚ + ๐Ÿ/๐Ÿ‘ ๐’Œ ฬ‚ 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‘– ฬ‚ + 2 ๐‘— ฬ‚ โˆ’ ๐‘˜ ฬ‚ and โ€“ ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ respectively, in the ratio 2 : 1 (ii) externally Position vector of R = (2(๐‘‚๐‘„) โƒ— โˆ’ 1(๐‘‚๐‘ƒ) โƒ—)/(2 โˆ’ 1) (๐‘‚๐‘…) โƒ— = (2(โˆ’๐‘– ฬ‚" + " ๐‘— ฬ‚" + " ๐‘˜ ฬ‚ )โˆ’1(๐‘– ฬ‚" + " 2๐‘— ฬ‚" โˆ’ " ๐‘˜ ฬ‚))/(2โˆ’1) (๐‘‚๐‘…) โƒ— = (โˆ’2๐‘– ฬ‚ + 2๐‘— ฬ‚ + 2๐‘˜ ฬ‚ โˆ’ ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + ๐‘˜ ฬ‚)/(2โˆ’1) (๐‘‚๐‘…) โƒ— = โ€“3๐’Š ฬ‚ + 3๐’Œ ฬ‚ Thus, Position vector of R dividing P and Q externally is โˆ’3๐‘– ฬ‚ + 3๐‘˜ ฬ‚

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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.