Add vectors of the same dimension component by component. The displayed vector sum includes enough working to inspect signs and scale.
It adds forces, velocities, coordinates, signals, and multidimensional changes.
Vector addition combines matching components and represents successive displacements or combined quantities.
On this page, the displayed vector sum follows this definition rather than any similarly named measure.
(1,2,3)+(4,−1,2)=(5,1,5).
Vectors must use the same dimension and coordinate basis before components can be combined. If the Vector Addition assumptions do not fit, consider directed difference.
When vector addition looks surprising, restore the sample and vary vector a by itself.
Align components, add each pair, and check the result dimension. Vector Addition also connects to result length.
Write each source value under its matching label before calculating: vector a and vector b. This preserves the assumptions behind vector sum and makes a later check possible without reopening the original problem.
Changing one component affects only its matching output component. This relationship remains useful even when the final vector sum is rounded.
Subtraction reverses the direction of the second vector contribution. The two results may share inputs while retaining different meanings.
Before publishing or sharing vector sum, decide on units, significant digits, and whether an exact form is expected. Those choices belong to interpretation rather than the calculator engine.
When reporting the answer, state the vector sum first, then its value and unit. Add vector a and vector b if someone else must verify the work independently.
The calculation behind Vector Addition starts from Vector a, and Vector b. Subtract either original vector from the sum to recover the other. Changing the order of the addends must not change the result.
For Vector Addition, save a dot-product, magnitude, or perpendicularity check that can reproduce the geometry. A geometric check places both vectors head to tail; the resultant should connect the initial tail to the final head. Reversing the addends must leave the component result unchanged. Adding the zero vector must also return the original vector.
Vector addition combines matching components and represents successive displacements or combined quantities.
It adds forces, velocities, coordinates, signals, and multidimensional changes.
Vectors must use the same dimension and coordinate basis before components can be combined.