Show that the tangent of a tangent is zero

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1. Express the scalar product of two blades in terms of the scalar product of their duals. It should only differ by a sign, which you should express in terms of the grade of the blades and the space they reside in.

2. What is the geometry of the element p ∧ u, where p is a point and u a Euclidean vector? (Hint: View it as a plunge. Counterhint: It is not the tangent vector o ∧ u moved to p.)

3. Show that the tangent of a tangent is zero. (Hint: Realize that a tangent is also a round; now use (15.1).)

Reference no: EM131008302

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