Examples
Examples
Try the starting example
- First real vector
- 1,2,3
- Second real vector
- 4,-5,6
- Dot product
- 12
- First vector Euclidean norm
- 3.741657
- Second vector Euclidean norm
- 8.774964
- Angle between vectors (degrees)
- 68.562447
Try another scenario
- First real vector
- 1,2,3
- Second real vector
- 0,0,0
- Dot product
- 0
- First vector Euclidean norm
- 3.741657
- Second vector Euclidean norm
- 0
- Angle between vectors (degrees)
- Undefined for a zero vector
Calculation method
Calculation method
Dot product
Sum matching component products.
First vector Euclidean norm
Square root of the sum of first-vector component squares.
Second vector Euclidean norm
Euclidean norm of the second vector.
Angle between vectors (degrees)
acos(dot/(norm1×norm2)), clamped for floating-point roundoff; undefined when either vector is zero.
Symbols and units
- a
- First real vector
- b
- Second real vector
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Equal-length finite real vectors in Euclidean coordinates. A zero vector has a dot product but no defined direction angle. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: dot product, norms and projection ↗
Background reading; this does not imply endorsement or independent review of SumFizz.