Vectors from a Centroid

★ 6/10plane geometry Polarization Identity vectors

Problem

A point $O$ in the plane of $\triangle ABC$ satisfies

\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} = \overrightarrow{0},

with $|\overrightarrow{OA}| = 2$ , $|\overrightarrow{OB}| = 3$ , $|\overrightarrow{OC}| = 4$ . Let $\theta$ be the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$ .

1. Find $\cos\theta$ . 2. Find $\overrightarrow{OA}\cdot\overrightarrow{OB} + \overrightarrow{OA}\cdot\overrightarrow{OC}$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Polarization Identity, vectors

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