Work out vector components instantly with clear inputs, formula shown and shareable results.
Resolving a vector splits it into perpendicular components. In the plane that is simply x = r·cos θ and y = r·sin θ; adding an elevation angle scales the horizontal part by cos φ and gives z = r·sin φ.
Components
x = r·cos φ·cos θ, y = r·cos φ·sin θ, z = r·sin φ
x = 40 and y = 30 — the 3-4-5 triangle scaled by ten. Adding elevation shrinks both by a factor of cos φ and lifts the rest into z.
Because the components are perpendicular, Pythagoras in three dimensions recovers the original length exactly.