From Mechanics

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Revision as of 17:39, 29 September 2010

\displaystyle \begin{align} & m(4\mathbf{i}+V\mathbf{j})+\lambda m(2\mathbf{i}-V\mathbf{j})=(m+\lambda m)(3\mathbf{i}+2\mathbf{j}) \\ & (4m+2\lambda m-3m)\mathbf{i}+(mV-\lambda mV-2\lambda m)\mathbf{j}=0\mathbf{i}+0\mathbf{j} \\ \end{align}

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

\displaystyle \begin{align} & 3m+2\lambda m-4=0 \\ & 2\lambda -1=0 \\ & \lambda =\frac{1}{2} \\ \end{align}