3D

Prove that line x=ay+b, z=cy+d and x= a'y+b', z=c'y+d' are perpendicular if aa'+cc'=-1( edited)

2 Answers

methinks there's a misprint in the sum it shud be aa' + cc' = -1

it goes this way...

x=ay+b or y = x - ba

z=cy+d or y = z - dc

so we get the first line as:

x - ba = y = z - dc

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similarly.........

x - b'a' = y = z - d'c'

so D.R of first line is < a, 1 , c>

and that of 2nd line is < a' , 1 , c' >

for them to be perpendicular

aa' + 1 + cc' = 0

or aa' + cc' = -1

thnx sandip..

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