52. (a) Use vector components to prove that two vectors commute for both addition and the scalar product. (b) Prove that two vectors anticommute for the vector product; that is, prove that AXB = -BXA.

52. (a) Use vector components to prove that two vectors commute for both addition and the scalar product. (b) Prove that two vectors anticommute for the vector product; that is, prove that AXB = -BXA.

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