Contribution to the magnetic field at the point by a thin wire

1. The problem statement, all variables and given/known data

A thin wire carries current along an arbitrary path, but when it passes through the origin, it is in the +y direction. Denote the magnitude of the current is 9.10A and we consider a point in space whose location is r = (-0.730m)*i + (0.390)*k.

Find the contribution to the magnetic field at the point being considered due only to the 0.500mm-long section of the wire centered at the origin.

The answer should be in the following format:
(dBx, dBy, dBz) = [ ] nT

2. Relevant equations

Biot-Savart Law:
(μo/4∏)*[I*(dL x r_hat)/(|r|^2)]

3. The attempt at a solution

So since there is no z-component in r, Bz should be 0. And since j x j = 0, By should also be 0.
For Bx, dl x r_hat should be r_vector/|r| -[itex]\widehat{k}[/itex] right?

I have a feeling I’m not doing the cross products correctly so I apologize in advance for my difficulty understanding this.

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