Misc 6
Last updated at March 20, 2018 by Teachoo
Transcript
Misc 6 If the lines ๐ฅ โ 1๏ทฎ โ 3๏ทฏ = ๐ฆ โ 2๏ทฎ2๐๏ทฏ = ๐ง โ 3๏ทฎ2๏ทฏ and ๐ฅ โ 1๏ทฎ3๐๏ทฏ = ๐ฆ โ 1๏ทฎ1๏ทฏ = ๐ง โ 6๏ทฎ โ 5๏ทฏ are perpendicular, find the value of k. Two lines ๐ฅ โ ๐ฅ1๏ทฎ ๐1๏ทฏ = ๐ฆ โ๐ฆ1๏ทฎ๐1๏ทฏ = ๐ง โ ๐ง1๏ทฎ๐1๏ทฏ and ๐ฅ โ ๐ฅ2๏ทฎ ๐2๏ทฏ = ๐ฆ โ ๐ฆ2๏ทฎ๐2๏ทฏ = ๐ง โ ๐ง2๏ทฎ๐2๏ทฏ are perpendicular to each other if ๐๐ ๐๐ + ๐๐ ๐๐ + ๐๐ ๐๐ = 0 Given, Since the two lines are perpendicular, ๐1 ๐2 + ๐1 ๐2 + c1๐2 = 0 (โ3 ร 3k) + (2k ร 1) + (2 ร โ 5) = 0 โ 9k + 2k โ 10 = 0 โ 7k = 10 k = โ๐๐๏ทฎ๐๏ทฏ Therefore, k = โ10๏ทฎ7๏ทฏ
Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise
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here, a1 should be -3๐ฅ