Cross product for parallel vectors

[adoado]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Line one 'direction' = (-2,4,4) = A
Line two 'direction' = (8,-1,4) = B

I remember that the cross product of two vectors is zero if they are parallel, but AxB is not the zero vector; the answer in the book says they are indeed parallel...

Is this not the right method?

Cheers,
Adrian ^^

 

[rock.freak667]

If they were parallel, you could write one direction as a scalar multiple of the other. Since you cannot do that as well as the cross-product is not zero, the vectors are not parallel.

 

[adoado]

Cheers, thanks for that. I got it all figured out now..

Thanks,
Adrian