Question

It is a vector question..
Find the angle between the lines (x-1)/2 = 1-y = 2z and x = y = 3z.

Answer 1

the lines are skew.

\[\frac{x-1}{2}=\frac{1-y}{1}=\frac{2z}{1}\] or \[\frac{x-1}{2}=\frac{y-1}{-1}=\frac{z-0}{1/2}\]

the vector parallel to the line is \[<2,-1,(1/2)>\]

similarly, the vector parallel to the line \[x=y=3z\] is \[<1,1,(1/3)>\]

find the angle between two vectors u and v by \[\Large \cos \theta = \frac{u\cdot v}{|u||v|}\]