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How to Calculate the Dot Product
Formula
The dot product sums the products of corresponding components: a . b = a1*b1 + a2*b2 + a3*b3.
The angle between vectors is found from cos(theta) = (a . b) / (|a| x |b|).
Common use cases:
- Calculating work done by a force
- Determining if vectors are perpendicular
- Projection of one vector onto another
Frequently Asked Questions
Dr. David Park
Applied Mathematician, PhD Mathematics
David holds a PhD in Applied Mathematics from MIT. He has published research on numerical methods and computational algorithms used in engineering and scientific calculators.
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