Vector Projection Calculator
Project vector a onto nonzero vector b in 2D or 3D; also find the signed scalar component.
Formula
proj_b(a) = [(a·b)/(b·b)]b; comp_b(a) = (a·b)/|b|.
Projection x ≈ (3)×(1) · Projection y ≈ (3)×(0) · Projection z ≈ (3)×(0) · Signed scalar component ≈ (3)÷sqrt((1))
How to use
- Enter a; use z = 0 for 2D.
- Enter a nonzero target direction b.
- Read the projected vector and signed component.
Examples
- a = (3,4,0), b = (1,0,0) gives projection (3,0,0).
Frequently asked questions
Which vector is projected?
a is projected onto the line directed by b.
Can b be the zero vector?
No. A target line needs a nonzero direction. The source a may be zero.
Why can the scalar component be negative?
It is negative when a points partly against b. Use the same Cartesian axes and component units.
Sources
Updated: