1. Using the definition of the dot product A B = A1B₁ + A2B2 + A3B3, prove that a) AB=BA; b) A. (B+C) = A·B+A C; c) A. (kB) = (kA) · B = k(AB).

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Subject : Theoretical Mechanics Topic: Dot Product Please provide all necessary solutions. [Letter C]
1. Using the definition of the dot product A B = A₁B1₁ + A₂B₂+ A3B3, prove that
a) AB=BA;
b) A. (B+C) = A·B+A·C;
c) A. (kB) = (kA) · B = k(A · B).
Transcribed Image Text:1. Using the definition of the dot product A B = A₁B1₁ + A₂B₂+ A3B3, prove that a) AB=BA; b) A. (B+C) = A·B+A·C; c) A. (kB) = (kA) · B = k(A · B).
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