Question

proof that axb= -(bxa)

Answer 1

Let \(a=\langle a_1,a_2,a_3\rangle\) and \(b=\langle b_1,b_2,b_3\rangle\).

Then
\[a\times b=\langle a_1b_2-a_2b_1, a_3b_2-a_2b_3, a_1b_3-a_3b_1\rangle\]
and
\[b\times a=\langle b_1a_2-b_2a_1, b_3a_2-b_2a_3, b_1a_3-b_3a_1\rangle\]
Clearly, \(a\times b=-(b\times a)\).

Answer 2

not sure if this is correct but i found the components for each side then substituted [1,0,0] as vector a and [0,1,0] as vector b and got 1= -(-1)