Vector Multiplication: Finding the Correct Solution

[Roodles01]

Homework Statement

Still having a little trouble so here's the problem.

(e_x + e_z) x (3e_y - 4ez)

The Attempt at a Solution

(e_x * e_z) + (e_x * (-4e_z)) + (e_z * 3e_y) + ( e_z * (-4e_z)

now, these are all orthogonal to each other, so, for example, if I have e_x * e_y then I should end up with e_z, shouldn't I?
So here is my solution.

= 3e_z - 4e_y + 3e_x - 4e_z
= 3e_x - 4 e_y + e_z

The solution shown to be correct is -3e_x + 4e_y + 3e_z

so what have I done wrong, please?

 

[Doc Al]

now, these are all orthogonal to each other, so, for example, if I have e_x * e_y then I should end up with e_z, shouldn't I?

I assume by * you mean X (vector product). So yes, $e_x \times e_y = e_z$. What about $e_y \times e_x$, $e_x \times e_z$, and the other combinations? (You are making a sign error.)

 

[Roodles01]

Thank you.
A simple thing becomes clear again.