A) \[\frac{3}{2}\]
B) \[\frac{9}{2}\]
C) \[-\frac{9}{2}\]
D) \[-\frac{3}{2}\]
Correct Answer: B
Solution :
Since, the lines intersect, therefore they must have a point in common, ie, \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}=\lambda \] (say) and\[\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{4}=\mu \] (say) \[\Rightarrow \]\[x=2\lambda +1,y=3\lambda -1,z=4\lambda +1\]and \[x=\mu +3,y=2\mu +k,z=\mu \]are same. \[\therefore \]\[2\lambda +1=\mu +3,3\lambda -1=2\mu +k\]and\[4\lambda +1=\mu \] On solving these, we get \[\lambda =-\frac{3}{2}\]and\[\mu =-5\] \[\therefore \] \[k=3\lambda -2\mu -1\] \[=3\left( -\frac{3}{2} \right)-2(-5)-1\] \[\therefore \] \[k=\frac{9}{2}\]You need to login to perform this action.
You will be redirected in
3 sec