Calculate the projection of vector u onto vector v.
Input Vectors
Projecting u onto v means finding the portion of u that points in v's direction.
Computed Projection
(4.00, 0.00)
Vector Projection (projᵥ u)
The component of u that lies along the direction of v.
Scalar Projection (compᵥ u)4.00
Dot Product (u·v)24
Vector u
Vector v
Projection
About this calculator
What is Vector Projection?
Vector projection is the process of finding the component of one vector (u) that lies in the direction of another vector (v). It's like finding the 'shadow' that vector u casts onto the line defined by vector v. It is used extensively in physics to break forces into components.
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Pro Tips
The scalar projection is the length of the projection vector (with a sign).
If the angle between u and v is acute, the projection is in the same direction as v.
If the angle is obtuse, the projection is in the opposite direction of v.
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Fun Facts
"Projections are a key part of the Gram-Schmidt process for finding orthonormal bases."
"In computer graphics, projections help calculate shadows and reflections on surfaces."
"The scalar projection is also called the 'component' of u along v."
