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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise

Transcript

Ex 11.2, 7 The Cartesian equation of a line is (๐‘ฅ โˆ’ 5)/3 = (๐‘ฆ + 4)/7 = (๐‘ง โˆ’ 6)/2. Write its vector form.Cartesian equation : (๐‘ฅ โˆ’ 5)/3 = (๐‘ฆ + 4)/7 = (๐‘ง โˆ’ 6)/2 (๐‘ฅ โˆ’ 5)/3 = (๐‘ฆ โˆ’ (โˆ’4))/7 = (๐‘ง โˆ’ 6)/2 Equation of a line in Cartesian form is given by (๐‘ฅ โˆ’ ๐‘ฅ1)/๐‘Ž = (๐‘ฆ โˆ’ ๐‘ฆ1)/๐‘ = (๐‘ง โˆ’ ๐‘ง1)/๐‘ Comparing (1) and (2), ๐‘ฅ1 = 5, ๐‘ฆ1 = โˆ’4, ๐‘ง1 = 6 ๐‘Ž = 3, b = 7, c = 2 Cartesian equation : (๐‘ฅ โˆ’ 5)/3 = (๐‘ฆ + 4)/7 = (๐‘ง โˆ’ 6)/2 (๐‘ฅ โˆ’ 5)/3 = (๐‘ฆ โˆ’ (โˆ’4))/7 = (๐‘ง โˆ’ 6)/2 Equation of a line in Cartesian form is given by (๐‘ฅ โˆ’ ๐‘ฅ1)/๐‘Ž = (๐‘ฆ โˆ’ ๐‘ฆ1)/๐‘ = (๐‘ง โˆ’ ๐‘ง1)/๐‘ Comparing (1) and (2), ๐‘ฅ1 = 5, ๐‘ฆ1 = โˆ’4, ๐‘ง1 = 6 ๐‘Ž = 3, b = 7, c = 2 Equation of line in vector form is ๐‘Ÿ โƒ— = ๐‘Ž โƒ— + ๐œ†๐‘ โƒ— Where ๐‘Ž โƒ— = ๐‘ฅ1๐‘– ฬ‚ + y1๐‘— ฬ‚ + z1๐‘˜ ฬ‚ = 5๐‘– ฬ‚ โˆ’ 4๐‘— ฬ‚ + 6๐‘˜ ฬ‚ & ๐‘ โƒ— = ๐‘Ž๐‘– ฬ‚ + b๐‘— ฬ‚ + c๐‘˜ ฬ‚ = 3๐‘– ฬ‚ + 7๐‘— ฬ‚ + 2๐‘˜ ฬ‚ Now, ๐‘Ÿ โƒ— = (5๐’Š ฬ‚ โˆ’ 4๐’‹ ฬ‚ + 6๐’Œ ฬ‚) + ๐œ† (3๐’Š ฬ‚ + 7๐’‹ ฬ‚ + 2๐’Œ 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.