(a) Use Exercises 1, 2, and 3 (or direct calculation) to prove that for any three vectors...

(a) Use Exercises 1, 2, and 3 (or direct calculation) to prove that

 

for any three vectors a, b, and c in ℝ3.

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(b) Show that

 

for any three vectors a, b, and c in ℝ3.

Exercises 1–3

1. Prove that .

2. Prove that

3. Prove that