Adding and Resolving Vectors

Interactive Simulator · Scalars and vectors

Add Them Tip to Tail

Two vectors add nose to tail: the resultant runs from the start of the first to the end of the second. Adjust each vector and watch the resultant, its perpendicular components, and its angle. The resultant equals the plain sum of the magnitudes only when both point the same way; at any angle between them it is shorter.

Mission Compare the resultant with the arithmetic sum |A| + |B|. Predict before revealing. Streak 0Best 0

|A| 7

angle A 0°

|B| 5

angle B 90°

Compared with the arithmetic sum |A| + |B|, the resultant magnitude is:

resultant Rx, Ry–

magnitude |R|–

direction (from +x)–

|R| = √(Rx² + Ry²), and the angle is tan⁻¹(Ry / Rx). The arithmetic sum |A| + |B| is the special case of parallel vectors.