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If 2 mutually perpendicular lines with their direction cosines are given then what will be the direction cosines of the third line which is perpendicular to both the given lines

If 2 mutually perpendicular lines with their direction cosines are given then what will be the direction cosines of the third line which is perpendicular to both the given lines 

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1 Answers

Sonu Kr Mishra Mishra AskIITian Expert -IITG
57 Points
13 years ago
let the two lines be ax + by + cz = d kx + ly + mz = n where a,b,c and k,l,m are the direction cosines of the two lines. the vectors parallel to the two lines are ai + bj + ck and ki + lj + mk now find the cross product of the two vectors to find the vector perpendicular to the them . let the cross product be Ai + Bj + Ck so the DCs of the line perpendicular to both the given lines is A/(A^2 + B^2 + C^2)^1/2 , B/(A^2 + B^2 + C^2)^1/2 , C/(A^2 + B^2 + C^2)^1/2 this question i have solved taking the general ref . it doesn't matter whether the given lines are perpendicular or not.

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