Question

The point of intersection of lines $\frac{x-4}{5}=\frac{y-1}{2}\frac{z}{1}$ and $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ is

• A. $(-1,-1,-1)$
• B. $(-1,-1,1)$
• C. $(1,-1,-1)$
• D. $noneofthese$

Answer 1

Answer: (A)

$(-1,-1,-1)$

$\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{1}$ and $\frac{x-2}{2}-\frac{y-2}{3}=\frac{z-3}{4}$

$(5\lambda +4,2\lambda +1,\lambda )$ $(2\mu +1,3\mu +2,4\mu +3)$

For point of intersection

$5\lambda +4=2\mu +1\Rightarrow (5\lambda -2\mu =-3)2$

$\lambda =4\mu +3$ $\lambda -4\mu =3$

$-$ $+$ $-$

___________________

$9\lambda =-6-3\Rightarrow \lambda =-1$

$(5\lambda +4,2\lambda +1,\lambda )\equiv (-1,-1,-1)$