CALCULATOR
2D Vector Projection Component onto Positive X Direction Vector Calculator
2D Vector Projection Component onto Positive X Direction Vector. Coordinate to return: X coordinate, Y coordinate only. Example: Source x: 3 units, Source y: 4 units, Target x: 1 number, Target y: 2 number, Coordinate to return: 1 selection gives 2.2 units. 2D source components same units; direction target dimensionless and target x≥.1 ensures nonzero; selected component. Only this original stated
2D source components same units; direction target dimensionless and target x≥.1 ensures nonzero; selected component. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Projection has source dot product along target with orthogonal residual.
Accepted inputs: Source x: -1,000 to 1,000 units; Source y: -1,000 to 1,000 units; Target x: 0.1 to 1,000 number; Target y: -1,000 to 1,000 number; Coordinate to return: choose X coordinate (1), Y coordinate (2).
2D Vector Projection Component onto Positive X Direction Vector
How the calculation works
projection=(source·target)/(target·target) target
Worked example
With source x 3 units, source y 4 units, target x 1 number, target y 2 number, coordinate to return X coordinate, 2d vector projection component onto positive x direction vector is 2.2 units.
Assumptions and limits
2D source components same units; direction target dimensionless and target x≥.1 ensures nonzero; selected component. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Projection has source dot product along target with orthogonal residual.