Let u(u1,u2,u3),v(v1,v2,v3) then u−v=a(u1−v1,u2−v2,u3−v3),
u+v=b(u1+v1,u2+v2,u3+v3) . a,b are ortogonal when the dot product
a⋅b=u12−v12+u22−v22+u32−v32=0 hence u12+u22+u32=v12+v22+v32
or ∣u∣=∣v∣. Next,
u,v are sides of a rhombus, u+v,u−v are diagonals of a rhombus.
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