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

Find 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.

Text Solution

Verified by Experts

The equations of straight lines can be rewritten as
`" "x=ay+b, z=cy+drArr(x-b)/(a)=(y-0)/(1)=(z-d)/(c)`
and `" "x=a'y+b', z=c'y+d'rArr(x-b')/(a')=(y-0)/(1)=(z-d')/(c')`
The above lines are perpendicular if `aa'+1*1+c*c'=0`.
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