Produit scalaire

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Cegep1

Mechanics

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46 words

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1 minute

Produit scalaire de $\vec{A}$ et de $\vec{B} = \vec{A} \cdot \vec{B} = | | \vec{A} | | \cdot | | \vec{B} | | \cos θ$

\begin{aligned} \vec{A} \cdot \vec{B} & = (A_{x} \hat{i} + A_{y} \hat{i}) \cdot (B_{x} \hat{j} + B_{y} \hat{j}) \\ = A_{x} B_{x} (\hat{i} \cdot \hat{i}) + A_{x} B_{y} (\hat{i} \cdot \hat{j}) + A_{y} B_{x} (\hat{j} \cdot \hat{i}) + A_{y} B_{y} (\hat{j} \cdot \hat{j}) \\ = A_{x} B_{x} + A_{y} B_{y} \end{aligned}

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