Mathegoras

Solid geometry › Polyhedra and sections › Angles in pyramids

Dot product in a regular tetrahedron

High school · ●●●○○ 50 pts

Given a regular tetrahedron P−ABCP-ABC with edge length 11, points E,F,G,HE, F, G, H lie on edges PA,PB,CA,CBPA, PB, CA, CB respectively. If EF→+GH→=AB→\overrightarrow{EF}+\overrightarrow{GH}=\overrightarrow{AB} and EH→⋅FG→=118\overrightarrow{EH} \cdot \overrightarrow{FG}=\frac{1}{18}, find EG→⋅FH→\overrightarrow{EG} \cdot \overrightarrow{FH}. Round to two decimal places.

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dot productregular tetrahedronisosceles trapezoid