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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 `
7 years ago

Sonu Kr Mishra Mishra AskIITian Expert -IITG
57 Points
```										 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.
```
7 years ago
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