|AB| = 1
|AC| = √2
∠BAC = 45°
AB·AC = |AB|*|AC|*cos∠BAC = 1*√2*(1/√2) = 1
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|AB| = 3
|AD| = 3
∠BAD = 120°
AB·AD = |AB|*|AD|*cos∠BAD = 3*3*(-1/2) = -9
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|BC| = 2
|BD| = √(AB²-AD²) = √(4-1) = √3
cos∠CBD = |BD|/|BC| = √3/2
BC·BD = |BC|*|BD|*cos∠CBD = 2*√3*(√3/2) = 3