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Question
Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are -2, 1, -1, and -3, -4, 1.
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Solution
Let a, b, c are the direction ratios of the required vector which is perpendicular to the vector with the direction ratio –2, 1, -1 and -3, -4, 1
– 2a + b - c = 0 and -3a - 4b + c = 0
`therefore a/(|[1,-1],[-4,1]|)=b/(|[-2,-1],[-3,1]|)=c/(|[-2,1],[-3,-4]|)`
`therefore a/(1-4)=-b/(-2-3)=c/(8+3)`
`a/(-3)=b/5=c/11`
The direction ratios of the required vector are (-3,5,11)
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