Vector Projection Calculator
Calculate orthogonal and parallel projections of vectors onto other vectors or subspaces
About this calculator
A Vector Projection Calculator computes the orthogonal and parallel projections of one vector onto another vector or subspace. This mathematical tool breaks down vectors into components that are parallel to and perpendicular to a given direction, which is essential in physics, engineering, and linear algebra. Vector projections help solve problems involving forces, motion analysis, data compression, and geometric transformations by decomposing complex vector relationships into simpler, more manageable components.
How to use
Enter the components of your source vector and the target vector or subspace onto which you want to project. The calculator will automatically compute both the parallel projection (component along the target) and orthogonal projection (perpendicular component). Results display the projected vector coordinates and magnitude values.
Frequently asked questions
What's the difference between orthogonal and parallel projections?
Parallel projection is the component of a vector along another vector's direction, while orthogonal projection is the perpendicular component remaining after subtracting the parallel projection.
Can I project vectors in 3D space?
Yes, this calculator supports vector projections in 2D and 3D space. Simply enter the x, y, and z components for three-dimensional calculations.
What are common applications of vector projections?
Vector projections are used in physics for force decomposition, computer graphics for lighting calculations, machine learning for dimensionality reduction, and engineering for structural analysis.