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find the direction ratios of line which is given as the line of intersection of the planes x+y+3z-5=0, 2x+y-7z+4=0.

find the direction ratios of line which is given as the line of intersection of the planes x+y+3z-5=0, 2x+y-7z+4=0.
 

Grade:12

2 Answers

Aishwarya
10 Points
7 years ago
eqn of intersection of 2 planes is ,(x+y+3z-5)+\lambda(2x+y-7z+4)=0
=>(1+2\lambda)x+(1+\lambda)y+(3-7\lambda)z+(-5+4\lambda)=0
=>dr’s=(1+2\lambda, 1+\lambda, 3-7\lambda)  where \lambda is a constant 
mycroft holmes
272 Points
7 years ago
The line of intersection of the two planes is perpendicular to the normals of the resp. planes i.e. to \vec{n_1} = i+j+3k and \vec{n_2} = 2i+j-7k. 
 
Hence it is parallel to their cross product \vec{n_1} \times \vec{n_2}. You can therefore find the direction ratios of the line of intersection

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