A charged particle carrying charge \(1 \mu \mathrm{C}\) is moving with velocity \((2 \hat{i}+3 \hat{j}+4 \hat{k}) \mathr…

A charged particle carrying charge \(1 \mu \mathrm{C}\) is moving with velocity \((2 \hat{i}+3 \hat{j}+4 \hat{k}) \mathrm{ms}^{-1}\). If an external magnetic field \((5 \hat{i}+3 \hat{j}-6 \hat{k}) \times 10^{-3} T\) exists in the region where the particle is moving then the force on the particle is \(\vec{F} \times 10^{-9} N\). The vector \(\vec{F}\) is:

[JEE Main 2023, 10 Apr (Shift 2)]