Components, Unit Vectors and Resolution

Any vector can be broken into pieces along the axes. A vector pointing up and to the right is just some amount of x plus some amount of y. Here you drag a vector and watch its components change, in flat 2D first and then in full 3D where a third piece appears along z.

Controls

Switch between 2D and 3D at the top. Drag the vector tip, or use the sliders — Ax from −8 to 8, Ay from −6 to 6, and in 3D an Az slider along the right edge of the screen. Reveals drop each component onto its axis, show the unit vectors î, ĵ and k̂, write A in î ĵ form, and in 3D show the direction cosines.

Variables and outputs

The component values, the magnitude, and the direction. Turn on the formula and it writes out A = Ax î + Ay ĵ with your actual numbers filled in. In 3D, turn on all three components and a box appears with the vector as its diagonal. Direction cosines shows α, β and γ, and that cos²α + cos²β + cos²γ always comes to 1.

Model assumptions

One vector only. No adding.

Learning objective

You should be able to write any vector in î ĵ k̂ form from its picture, and read the picture back from the form.