Section 12.2: Vectors

Let C be the point on the line segment AB that is twice as far from B as it is from A. If \(\mathbf{a} = \vec{OA}, \mathbf{b} = \vec{OB},\) and \(\mathbf{c} = \vec{OC}\), show that \(\mathbf{c} = \frac{2}{3}\mathbf{a} + \frac{1}{3}\mathbf{b}\).