Verify (a + a) × (a+ b) = 0⃗ . What can be said about two vectors whose cross product is the zero vector

Question

a x b

= i j k
3 -3 1
-12 12 -4

=
i
( (-3) · (-4) - 1 · 12 ) -
j
( 3 · (-4) - 1 · (-12) ) +
k
( 3 · 12 - (-3) · (-12) ) =
=
i
( 12 - 12 ) -
j
( (-12) - (-12) ) +
k
( 36 - 36 ) =
=
(0 ; 0 ; 0)

2. Relevant equations

have i correctly verified with an example that two vectors whose cross product is the zero vector?

Answer 1

that looks right....what can be said about them is that they are parallel in space