Question

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ are interesting, then k =

• A. $\frac{-7}{2}$
• B. $\frac{7}{2}$
• C. $\frac{-9}{2}$
• D. $\frac{9}{2}$

Answer 1

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

$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}=lx=1+2l,y=-1+3l,z=1+4l\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}=mx=3+m,y=k+2m,z=m$

If they are intersecting, they will have a point in common

$1+2l=3+m1+4l=m2l-m=2-\left(i\right)4l-m=-1-\left(ii\right)\left(i\right)-\left(ii\right)-2l=3l=\frac{-3}{2}m=2l-2=2\left(\frac{-3}{2}\right)=-5k+2m=-1+3lk+2(-5)=-1+3\left(\frac{-3}{2}\right)k-10=-1-\frac{9}{2}k-10=\frac{-11}{2}k=10-\frac{11}{2}\therefore k=\frac{9}{2}$