Prove that for any vectors u, v, and w in R2 or R3 and any scalar c,

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Prove that for any vectors u, v, and w in R2 or R3 and any scalar c, we have
(a) (u + cv) ∙ w = u ∙ w + c(v ∙ w);
(b) u ∙ (cv) = c(u ∙ v);
(c) (u + v) ∙ (cw) = c(u ∙ w) + c(v ∙ w).
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