parallel lines?

[mathstresser]

Is the line through (-4,-6,1) and (-2,0,-3) parallel to the line through (10,18,4) and (5,3,14)?

I get the slope of the first two to be <-6,6,4> and the last two to be <5,15,-10>.

I change these two to be 2<-3,-3,2> and 5<1,3,-2>. I think that that shows it is not parallel, but the answer says, "yes, it is parallel" What did I do wrong?

 

[soroban]

Hello, mathstresser!

A tiny arithmetic error . . .

Is the line through A(-4,-6,1) and B(-2,0,-3) parallel to the line through C(10,18,4) and D(5,3,14)?

\(\displaystyle \vec{AB}\:=\:\langle2,6,-4\rangle\:=\:2\langle1,3,-2\rangle\)

\(\displaystyle \vec{CD}\:=\:\langle-5,-15,10\rangle\:=\:-5\langle1,3,-2\rangle\)

. . . They are parallel.

 

[mathstresser]

Thank you!

I can do calc 2 (for the most part, anyway)... but I can't find -2-(-4)... :roll: