MathDB
2000 Oral #9: Three dimensional vectors

Source:

October 6, 2014
vectortrigonometrygeometry3D geometryspheregeometric transformationrotation

Problem Statement

Let v1⃗,v2⃗,v3⃗,v4⃗\vec{v_1},\vec{v_2},\vec{v_3},\vec{v_4} and v5⃗\vec{v_5} be vectors in three dimensions. Show that for some i,ji,j in 1,2,3,4,51,2,3,4,5, vi⃗⋅vj⃗≥0\vec{v_i}\cdot \vec{v_j}\ge 0.
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