Question

Question #194ef

Answer 1

They are parallel and the distance between them is `5/sqrt6`.

Explanation:

the given lines can be written as follows :

L1 = <2,3,4> + t <-1,2,1> = (x1 ,y1 ,z1) + t * (a,b,c)
L2 = <3,1,4> + t <3,-6,-3> = (x2 ,y2 ,z2) + t* (d,e,f)

Two lines are parallel if their direction ratios(known ad DR's) are proportional to each other.
<a,b,c> are the DR's of L1 and <d,e,f> are DR's of L2.
Note how `a/d = b/e = e/f = -1/3`.
That says the lines are parallel .

Awesome , now to calculate the distance :

distance between parallel lines is given by
`abs((<(x2-x1),(y2-y1), (z2-z1)> . <(a),(b),(c)>)/ abs(vec b))`

Note that you can also use (d,e,f) instead of (a,b,c) in the above formula .
I am skipping the calculations.
The answer is `abs(-5/sqrt6) = 5/sqrt6` .