Vector Addition

Place vectors on a plane and see the resultant from head-to-tail or component addition. Reinforces magnitude, direction, and decomposition.

Who it's for: Physics and engineering prep; first-week vector skills.

Key terms

  • vector
  • resultant
  • components
  • head-to-tail
  • magnitude

How it works

Vectors add component-wise: R = A + B means R_x = A_x + B_x and R_y = A_y + B_y. Geometrically, place the tail of B at the head of A (or use the parallelogram rule). The cyan arrow shows the resultant.

Key equations

A_x = |A| cos θ,   A_y = |A| sin θ
R_x = A_x + B_x,   R_y = A_y + B_y