Free · Algebra and geometric models

Weighted Vector Sums and Differences

Add or subtract two vectors in Cartesian 2D or 3D coordinates, with optional scalar multiples and 2D polar input.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked inputs, x = 3, y = 4, Magnitude (m) = 5.

R=αA±βB; |R|=√(Rx²+Ry²); direction=atan2(Ry,Rx)

Worked example

Enter these known values and leave the other values blank.

Vectors in
2
Operation
1
2
Vector representation
0
x
3
y
0
x
0
y
4
x
3
y
4

Assumptions and limitations

  • Coordinates and scalar coefficients may be signed. A zero vector has no direction.
  • Polar magnitude is nonnegative and its direction uses the principal atan2 branch. Captured sine/cosine component magnitudes below 10⁻¹⁵ are set to zero.

Common questions

What must I enter?

Choose the mode when available and enter its independent known quantities. Leave an unknown editable quantity empty to use a supported inverse.

How should I use the result?

Interpret the numbers within the stated mathematical assumptions. Available unit selectors convert quantities; display rounding does not replace the internal calculation.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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