Given two nonzero vectors a and b in ℝ3, show that v1= a/∥a∥, v2 = a × b/∥a × b∥, and v3 = a × (a × b)/(∥a∥∥a × b∥) are mutually orthogonal and that they form a right-handed system in that v1 × v2 = v3, v2 × v3= v1, and v3 × v1= v2.
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