must show that 0 x a and a x 0 = 0 for any vector a in V3
so would this be sufficient:
<0, 0, 0> x <1, 2, 3> = 0
and <2, 3, 4> x <0, 0, 0> = 0
because
0 - 0 + 0 = 0
correct?
believe this is cross product stuff.
must show that 0 x a and a x 0 = 0 for any vector a in V3
so would this be sufficient:
<0, 0, 0> x <1, 2, 3> = 0
and <2, 3, 4> x <0, 0, 0> = 0
because
0 - 0 + 0 = 0
correct?
believe this is cross product stuff.
No. All you have shown is that this is true for a few vectors. You need to prove that it is true for all vectors.
To show this, you let be any general vector with components:
So let's take the cross product:
Do the same with .
Both of these should be equal to 0 and since was a general vector, then it must be true for any vector in .