Vector operations
Addition and subtraction work component-wise. The dot product returns a scalar. The cross product (3D only) returns a perpendicular vector. Scalar multiplication scales each component.
Vector Calculator
Perform vector operations including addition, subtraction, dot product, cross product, and scalar multiplication.
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Dimensions
Operation
Vector 1
Vector 2
Real-valued vectors only
This calculator works with real number components. Complex-valued vectors are not supported.
Cross product is 3D only
The cross product is defined for three-dimensional vectors. Switch to 3D mode to use it.
Result
(4, 6)
Sum of the input vectors.
- |v1| magnitude
- 5
- |v2| magnitude
- 2.2361
- |result| magnitude
- 7.2111
- Component x
- 4
- Component y
- 6
Step-by-step
- v1 = (3, 4)
- v2 = (1, 2)
- v1 + v2 = 3 + 1, 4 + 2
- Result = (4, 6)
Also in Linear Algebra
Linear Algebra
Vector calculator: perform multiple vector operations
A general-purpose vector calculator that performs addition, subtraction, dot product, cross product, and scalar multiplication on 2D or 3D vectors.
Frequently asked questions
Addition, subtraction, cross product, and scalar multiplication return vectors. The dot product returns a scalar (a single number).
The cross product is defined only in three dimensions because it produces a vector perpendicular to both inputs, which requires a third dimension.
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