Consider the tetrahedron spanned by vectors a, b, and c as in Figure25(A). Let A, B, C be the faces containing the origin 0, and let D bethe fourth face opposite O. For each face F, let v F be the vector that isperpendicular to the face, pointing outside the tetrahedron, of magnitudeequal to twice the area of F. Prove the relationsVA+ VB+ vc =ax b +bx c + c x aVA +vB +vc +vv = 0Hint: Show that vv = (c - b) x (b - a).

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