# Thread: [SOLVED] Two simple problems

1. ## [SOLVED] Two simple problems

You're not supposed to use vector/scalar multiplication tricks for these problems.

1) The point C divides the vector AB in the ratio 1:3. Show that $\displaystyle \overline{OC} = \frac{3}{4}\overline{OA} + \frac{1}{4}\overline{OB}$

2) $\displaystyle u,\ e_1,\ e_2$ are in the same plane.

$\displaystyle |u| = 2, |e_1| = 2, |e_2| = 1$
The angle between $\displaystyle e_1$ and $\displaystyle e_2$ is $\displaystyle \frac{2\pi}{3}$, and $\displaystyle \frac{\pi}{6}$ between $\displaystyle u$ and $\displaystyle e_1$.

Write $\displaystyle u$ as a linear combination of $\displaystyle e_1$ and $\displaystyle e_2$.

Note that this will give two possible answers.

2. 1)

$\displaystyle \overline{AB} = \overline{OB} - \overline{OA}$

$\displaystyle \overline{OC} = \overline{OA} + \frac{1}{4}\overline{AB}$

$\displaystyle \overline{OC} = \overline{OA} + \frac{1}{4}(\overline{OB} - \overline{OA}) = \frac{3}{4}\overline{OA} + \frac{1}{4}\overline{OB}$