Proving the Cross Product of Non-Zero Parallel Vectors is Equal to 0

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cleopatra
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Homework Statement


F and G are not 0.
F and G are parallel
Proof that F X G is=0


Attempt for a sol:

F=(a1,b1,c1)
G=(a2,b2,c2)
FXG=...
But then I don´t know how to show that they are parallel.

Or..

Find some numbers for F and G that I know that makes them parallel and show that FXG
are=0
But I think I´m not supposed to use numbers, but a,b,c...

Would you use either one of theses attempts or not?
 
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There are several different definitions of vectors being parallel (one of them is that the outer product is zero).
So can you check your notes / textbook and tell us what it means if two vectors are parallel.

If it says something like: "F and G are parallel if there is some number c such that F = c G" then you can simply take
F = (x, y, z)
G = (cx, cy, cz)
and compute the cross product.

(Note that this is completely general because the cross product only exists in 3 dimensions)