What Is the Electromagnetic Force on an Electron in Given Fields?

[Roodles01]

Homework Statement

An electron in an electric field E = 3.0x10⁷ e_x NC^-1 and a magnetic field B = 3.0 e_z T has velocity v = 1.0x10⁷ (2e_x - e_y) ms^-1.

Calculate electromagnetic force on the electron.

Homework Equations

F = q (E + v X B)
where q = e^- = -1.6x10^-19 C

The Attempt at a Solution

I have attached a working out, but have difficulty with just one aspect.

Whilst working out the matrix vXB I have a negative sign where I think a positive sign should be.
I have attached the working as a pic.
Could someone show me why I am correct or incorrect.
Thank you.

 

[Roodles01]

Ah! Is this to do with e_x X e_y = -e_y?
They're orthogonal?

 

[ap123]

The negative sign comes from the definition of the cross product.
v x B = e_x(...) - e_y(...) + e_z(...)

 

[Roodles01]

Again, I have to go "Doh!"
Thank you.