**b**and the length of other side is equal to the projection of vector

**a**onto

**b**. They discover that the signed area of this rectangle is equal to the product of the magnitude of

**a**, the magnitude of

**b**, and the cosine of the angle between them. They can then use the angle difference identity for cosine to show that this is equal to the sum of the product of the x-components and the product of the y-components.

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