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Fid the condition if lines x=a y+b ,z=c ...

Fid the condition if lines `x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d '` are perpendicular.

A

`aa'+c c'=1`

B

`a/a'+c/c'=-1`

C

`(a)/(a')+(c)/(c')=1`

D

aa'+cc'=-1

Text Solution

Verified by Experts

The correct Answer is:
D
Given equation of lines are `x=ay+b, z=cy+d`
and `x=a'y=+b',z=c'y+d'`
These equations can be rewritten as `(x-b)/(a)=(y-0)/(1)=(z-d)/(c) and (x-b')/(a')=(y-0)/(1)=(z-d')/(c')`
These lines will perpendicular, if `aa'+1+c c'=0 [therefore a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=0]`
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