You have done the cross product incorrectly. The j coefficient is the negative of the minor.
Using the Lorentz force law for my problem, I get the following matrix.
I ex ey ez I
I 1 . -1 . 0 I
I 1 . 0 . -1 I
I have evaluated the ey term as a -ve ( ey((1X-1)-(0x1)) = ey(-1-0) = -1ey)
= ex((-1x-1)-(0x0)) + ey((1X-1)-(0x1)) + ez ((1x0)-(-1x1))
= e_{x} - e_{y} + e_{z }Another person evaluates this term as +ve. so could someone point out the obvious mistake I made, please, I can't see it.
The set problem is
An electron in a magnetic field B=2.0T(e_{x}-e_{z}) has velocity v=(2.5x10^{7} ms-1 (e_{x}-e_{y})
a) calculate magnetic force on electron at that instant
Now, F = -e 2(2.5x10^{7}) (e_{x}-e_{z})* (e_{x}-e_{y})
so
F = -8x10-12 (e_{x} - e_{y} + e_{z})