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Projection of One 3D Vector onto Another — result sheet
Calculate the vector projection of A onto nonzero vector B from their ordered three-dimensional components.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: proj_B(A) = (A dot B)/(B dot B) B.
The vector projection of A onto nonzero B is the component of A parallel to B. The scalar dot-product ratio multiplies each ordered component of B.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vector A x — The x component of vector A.; minimum -1000000; maximum 1000000
- Vector A y — The y component of vector A.; minimum -1000000; maximum 1000000
- Vector A z — The z component of vector A.; minimum -1000000; maximum 1000000
- Vector B x — The x component of vector B.; minimum -1000000; maximum 1000000
- Vector B y — The y component of vector B.; minimum -1000000; maximum 1000000
- Vector B z — The z component of vector B.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Vector A x | 3 |
| Vector A y | 4 |
| Vector A z | 0 |
| Vector B x | 1 |
| Vector B y | 0 |
| Vector B z | 0 |
The projection of A onto B is (3, 0, 0).
Assumptions and limits
- A and B are Cartesian 3D vectors in one common Euclidean basis, and B is nonzero.
- The result is a geometric projection only; no unit conversion, physical force decomposition, or perpendicular component is inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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