Discussion Forum



1)

The two liines x=my+n, z=py+q  and x=m'y+n', z=p'y+q' are perpendicular to each other, if


A) $mm'+pp'=1$

B) $\frac{m}{m'}+\frac{p}{p'}=-1$

C) $\frac{m}{m'}+\frac{p}{p'}=1$

D) $mm'+pp'=-1$

Answer:

Option D

Explanation:

Given lines are

 x=my+n,z=py+q   and x=m'y+n'. z=p'y+q'

 Above equations can be rewritten as 

$\frac{x-n}{m}=\frac{y-0}{1}=\frac{z-q}{p}$  and  

 $\frac{x-n'}{m}=\frac{y-0}{1}=\frac{z-q'}{p'}$

Lines will be perpendicular , if

 mm'+1+pp'=0

$\Rightarrow$     mm'+pp'=-1