A straight thin wire carrying a current of $I=1 \mathrm{~A}$ in the direction $\widehat{n}=\dfrac{1}{\sqrt{6}} \hat{\imath}+\dfrac{2}{\sqrt{6}} \hat{\jmath}+\dfrac{1}{\sqrt{6}} \hat{k}$ is placed inside a magnetic field of $\vec{B}=(2 \hat{\imath}+2 \hat{k}) \mathrm{T}$. The force per unit length on the wire is $\_\_\_\_$ $\mathrm{N} / \mathrm{m}$.
- $2 \sqrt{6} \hat{\imath}-2 \sqrt{6} \hat{k}$
- $\sqrt{\dfrac{3}{2}} \hat{\imath}-\sqrt{\dfrac{3}{4}} \hat{\jmath}+\sqrt{\dfrac{3}{4}} \hat{k}$
- $\dfrac{4}{\sqrt{6}} \hat{\imath}-\dfrac{4}{\sqrt{6}} \hat{k}$
- $\sqrt{\dfrac{3}{2}} \hat{\imath}+\sqrt{\dfrac{3}{4}} \hat{\jmath}+\sqrt{\dfrac{3}{4}} \hat{k}$
