If the lines x=ay+b, z=cy+d and x=a'z+b', y=c'z+d' are perpendicular, then:

Question

If the lines $x=ay+b,\ z=cy+d$ and $x=a'z+b',\ y=c'z+d'$ are perpendicular, then:

Accepted Answer

Equation of 1st line is

$${{x - b} \over a} = {y \over 1} = {{z - d} \over c}$$

Dr's of 1st line = ($a$, 1 , c)

Equation of 2nd line is

$${{x - b'} \over {a'}} = {{y - b'} \over {c'}} = {z \over 1}$$

Dr's of 2nd line = ($a'$, c' , 1)

Lines are perpendicular, so the dot product of the Dr's of two lines are zero.

$$ \therefore $$ $aa$' + c + c' = 0

Solutions · 1