Parametric, Polar & Vectors · Vector Operations
Vector Projection
The projection of u onto v gives the component of u in the direction of v.
Variables
| Symbol | Name | Unit |
|---|---|---|
| u1 | u x-component | — |
| u2 | u y-component | — |
| v1 | v x-component | — |
| v2 | v y-component | — |
Worked examples
Find proj_v u where u = ⟨3, 4⟩ and v = ⟨1, 0⟩.
- u · v = 3. |v|² = 1.
- proj = (3/1)⟨1, 0⟩ = ⟨3, 0⟩
Answer: ⟨3, 0⟩
Find proj_v u where u = ⟨2, 3⟩ and v = ⟨1, 1⟩.
- u · v = 2+3 = 5. |v|² = 2.
- proj = (5/2)⟨1, 1⟩ = ⟨5/2, 5/2⟩
Answer: ⟨5/2, 5/2⟩
Practice this and 135 more formulas in the CalcRef workspace — quizzes, reference tables, a 16-category unit converter, and an expression evaluator.