From Mechanics

From part a)

\displaystyle (5m+2\lambda m-3m-3\lambda m)\mathbf{i}+(mV-\lambda mV+2m+2\lambda m)\mathbf{j}=0\mathbf{i}+0\mathbf{j}

Consider the \displaystyle \mathbf{j} component. That is the \displaystyle \mathbf{j} component on the left hand side must be the same as the \displaystyle \mathbf{j} component on the right hand side, that is zero.

\displaystyle \begin{align} & mV-\lambda mV+2m+2\lambda m=0 \\ & V-2V+2+4=0 \\ & -V+6=0 \\ & V=6 \\ \end{align}

Note that \displaystyle V is a dimensionless number.