c
\(\overrightarrow{ F }=q(\overrightarrow{ V } \times \overrightarrow{ B })\) (Force on charge particle moving in magnetic field)

\(\overrightarrow{ V } \times \overrightarrow{ B }=(2 \hat{ i }+3 \hat{ j }+4 \hat{ k }) \times(5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\)

\(=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 4 \\ 5 & 3 & -6\end{array}\right| \times 10^{-3}\)

\(=[\hat{i}[-18-12]-\hat{j}[-12-20]+\hat{k}[6-15]] \times 10^{-3}\)

\(=[\hat{i}[-30]+\hat{j}[32]+\hat{k}[-9]] \times 10^{-3}\)

Force \(=10^{-6}[-30 \hat{i}+32 \hat{j}-9 \hat{k}] \times 10^{-3}\)

\(=10^{-9}[-30 \hat{ i }+32 \hat{ j }-9 \hat{ k }]\)