If (vec{A}=A_{x} hat{i}+A_{y} hat{jmath}) and (vec{B}=B_{x} hat{i}+B_{y} hat{jmath}), show that (vec{A} cdot vec{B}=) (A_{x} B_{x}+A_{y} B_{y}). You

Question:

If $\vec{A}=A_{x} \hat{i}+A_{y} \hat{\jmath}$ and $\vec{B}=B_{x} \hat{i}+B_{y} \hat{\jmath}$, show that $\vec{A} \cdot \vec{B}=$ $A_{x} B_{x}+A_{y} B_{y}$. You may wish to use the fact that the scalar product satisfies the distributive property: $\vec{a} \cdot(\vec{b}+\vec{c})=$ $\vec{a} \cdot \vec{b}+\vec{a} \cdot \vec{c}$.)

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