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Find the Direction Ratios of a Vector Perpendicular to the Two Lines Whose Direction Ratios Are -2, 1, -1, and -3, -4, 1. - Mathematics and Statistics

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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)

Concept: Basic Concepts of Vector Algebra
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