Dot Product

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The dot product of vectors a⃗ and b⃗ is defined as

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1. **Scalar Product Definition**: The dot product results in a scalar value.
2. **Geometric Formula**: $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$, where $	heta$ is the angle between the two vectors.
3. **Physical Meaning**: It represents the projection of one vector onto the other multiplied by the other's magnitude.
4. **Range**: Value is positive for acute angles, zero for orthogonal vectors, and negative for obtuse angles.

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