Finding Resultant Force

Calculus 3 · Axiom Academy

EXAMPLE Finding Resultant Force Add three force vectors component-by-component, then find the resultant's magnitude and unit vector. Three forces act on a single particle: Find the resultant force , its magnitude , and the unit vector that points in its direction. Placing the three forces head-to-tail (using the xy -projection so it can be drawn) traces a path from the origin to . The resultant is the straight arrow from start to finish. 2D projection for visualization only — the worked solution below keeps all three components. Nice work — you built the resultant force from its three sources and described it completely. Component-wise addition: Add vectors one axis at a time — all the i -components, then all the j -components, then all the k -components. Resultant force: is the single net force equivalent to all three acting together. Magnitude: — the 3-D Pythagorean theorem gives the strength of that net force. Unit vector: strips out the size and keeps only the direction (its own magnitude is 1 ). The magnitude tells you how hard the particle is pushed; the unit vector tells you which way it accelerates. The same recipe works for any vector quantity — velocity, displacement, or electric field.

This is the written version of the interactive lesson above. See the full Calculus 3 course.