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Misc 6 - If lines are perpendicular, find value of k - Miscellaneous

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Misc 6 If the lines ๐‘ฅ โˆ’ 1๏ทฎ โˆ’ 3๏ทฏ = ๐‘ฆ โˆ’ 2๏ทฎ2๐‘˜๏ทฏ = ๐‘ง โˆ’ 3๏ทฎ2๏ทฏ and ๐‘ฅ โˆ’ 1๏ทฎ3๐‘˜๏ทฏ = ๐‘ฆ โˆ’ 1๏ทฎ1๏ทฏ = ๐‘ง โˆ’ 6๏ทฎ โˆ’ 5๏ทฏ are perpendicular, find the value of k. Two lines ๐‘ฅ โˆ’ ๐‘ฅ1๏ทฎ ๐‘Ž1๏ทฏ = ๐‘ฆ โˆ’๐‘ฆ1๏ทฎ๐‘1๏ทฏ = ๐‘ง โˆ’ ๐‘ง1๏ทฎ๐‘1๏ทฏ and ๐‘ฅ โˆ’ ๐‘ฅ2๏ทฎ ๐‘Ž2๏ทฏ = ๐‘ฆ โˆ’ ๐‘ฆ2๏ทฎ๐‘2๏ทฏ = ๐‘ง โˆ’ ๐‘ง2๏ทฎ๐‘2๏ทฏ are perpendicular to each other if ๐’‚๐Ÿ ๐’‚๐Ÿ + ๐’ƒ๐Ÿ ๐’ƒ๐Ÿ + ๐’„๐Ÿ ๐’„๐Ÿ = 0 Given, Since the two lines are perpendicular, ๐‘Ž1 ๐‘Ž2 + ๐‘1 ๐‘2 + c1๐‘2 = 0 (โˆ’3 ร— 3k) + (2k ร— 1) + (2 ร— โˆ’ 5) = 0 โˆ’ 9k + 2k โˆ’ 10 = 0 โˆ’ 7k = 10 k = โˆ’๐Ÿ๐ŸŽ๏ทฎ๐Ÿ•๏ทฏ Therefore, k = โˆ’10๏ทฎ7๏ทฏ

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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
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