Question

Find value of $k$ if the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$

• A. $\frac{3}{2}$
• B. $\frac{9}{2}$
• C. $-\frac{2}{9}$
• D. $-\frac{3}{2}$

Answer 1

The correct option is B $\frac{9}{2}$

To Find : value of k.

$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}=m$

$x=2m+1;y=3m-1;z=4m+1$

$\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}=n$

$x=n+3;y=2n+k;z=n$

$2m+1=n+3$

$n=2m-2$

$4m+1=n$

$4m+1=2m-2$

$2m=-3\Rightarrow m=\frac{-3}{2}$

$n=-5$

$3m-1=2n+k$

$\frac{3(-3)}{2}-1=2(-5)+k$

$\frac{-11}{2}=-10+k$

$k=\frac{-11}{2}+10$

$k=\frac{9}{2}$