Question

The lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{1}=\frac{y}{3}=\frac{z}{4}$ are

• A. Parallel
• B. Intersecting
• C. Skew
• D. At right angles

Answer 1

Answer: (C)

Skew

$ratioofdirectionratio\left(\frac{1}{1}\right)\ne \left(\frac{2}{3}\right)\ne \left(\frac{3}{4}\right)hencelinesarenotparallelletbothintersect,then\left(\frac{x-1}{1}\right)=\lambda orx=\lambda +1and\left(\frac{x+1}{1}\right)=\mu andx=\mu -1\lambda +1=\mu -1or\mu =\lambda +2then\left(\frac{y-2}{2}\right)=\lambda ory=2\lambda +2and\left(\frac{y}{3}\right)=\mu \therefore y=3\mu or2\lambda +2=3\mu or2\lambda +2=3\lambda +6\therefore \lambda =-4alsoz=3\lambda +3=-9butz=4\mu =4(-2)=-8\therefore -9\ne -8hencelineareskewlines$