Question

Multiple choice.
How would I answer this in a short way?
what is the distance between the skew lines L1:(0,4,-3)+s(-1,1,3),seR and L2: (1,2,5)+t(-3,2,5),teR?

a) 4 root 2
b) 7/2
c) root 2
d) (7 root 2)/2

Answer 1

as your text no doubt shows, given the two lines

L1 = <b>a</b>+<b>b</b>s
L2 = <b>c</b>+<b>d</b>t

the distance between the lines is given by

(<b>a</b>-<b>c</b>).(<b>b</b>x<b>d</b>)/|<b>b</b>x<b>d</b>|

In this case, that is

(-1,2,-8).(-1,1,3)x(-3,2,5)/|(-1,1,3)x(-3,2,5)| = 15/3√2 = 5/√2

Hmmm. Better check my math.

Answer 2

To Sara:
I got 5/√2 as well. Perhaps it is time to check if there are typos in the question or the answer.

Also, to print s∈R, you can write
s & i s i n ; R, but skip the spaces.