Methane Dot Products

★ 5/10Polarization Identity solid geometry Symmetry vectors

Problem

In a methane molecule $\mathrm{CH}_4$ , the four hydrogen atoms sit at the vertices $H_1, H_2, H_3, H_4$ of a regular tetrahedron with edge length $1$ , and the carbon atom sits at the center $C_0$ . Find

\sum_{1 \leqslant i < j \leqslant 4} \overrightarrow{C_0H_i} \cdot \overrightarrow{C_0H_j}.

Answer

Solution

Difficulty	5/10
Topics	Polarization Identity, solid geometry, Symmetry, vectors

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