How this calculator works
Vector combinations act on corresponding components. Planar polar inputs are first converted with cosine and sine. Displacement subtracts the first position from the second and ignores the combination multipliers. Recovery rearranges the component equation, requiring a nonzero multiplier for the missing vector. A missing multiplier needs a nonzero known vector and consistent component equations within a relative tolerance of 1e-10. A zero result is valid but has no direction angle.
Formula
R = alpha A + beta B or alpha A - beta B. Planar components are (m cos(theta), m sin(theta)). Displacement P to Q = Q - P.
Worked example
Adding (1, 2) and (3, 4) gives (4, 6), with magnitude sqrt(52). Subtracting them in that order gives (-2, -2). A 3-unit east vector plus a 4-unit north vector gives (3, 4), of length 5.
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Frequently asked questions
Can I add a 2D vector to a 3D vector?
Use matching lengths. If a planar vector belongs in 3D space, append a zero z component.
What does a negative multiplier do?
It reverses that vector before scaling its length.
Which way are angles measured?
Positive angles turn anticlockwise from the positive x axis. The result uses the range 0 to less than 360 degrees.