Parametric, Polar & Vectors · Vector Operations

Vector Projection

projvu=uvv2v\text{proj}_{\vec{v}} \vec{u} = \frac{\vec{u} \cdot \vec{v}}{|\vec{v}|^2} \vec{v}

The projection of u onto v gives the component of u in the direction of v.

  • 4 variables
  • 2 worked examples
  • 12 in Parametric, Polar & Vectors

Variables

Variables used in the Vector Projection formula
SymbolNameUnit
u1u x-component -
u2u y-component -
v1v x-component -
v2v y-component -

Worked examples

Find proj_v u where u = ⟨3, 4⟩ and v = ⟨1, 0⟩.
  1. u · v = 3. |v|² = 1.
  2. proj = (3/1)⟨1, 0⟩ = ⟨3, 0⟩

Answer: ⟨3, 0⟩

1 more worked examplePremium

Find proj_v u where u = ⟨2, 3⟩ and v = ⟨1, 1⟩.

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Practice

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