Question

lf the d.r's of two lines are given by the equations $l+m-n=0$ and $l^2+m^2-n^2=0$, then the d.r's of one of the two lines are:

• A. $0,0,-1$
• B. $0,1,-1$
• C. $1,0,1$
• D. $1,0,0$

Answer 1

The correct option is C $1,0,1$

Given that $l+m=n$
Substituting $n$ in $l^2+m^2-n^2=0$, we get

$l^2+m^2-(l+m{)}^2=0$
$\Rightarrow lm=0$
$\Rightarrow l=0$ or $m=0$
Substituting in $l+m=n$, we get

$m=n$ or $l=n$
Now, $(l,m,n)=(0,n,n)$ or $(n,0,n)$
Therefore, d.r.s are $(0,1,1)$ or $(1,0,1)$
Ans: B