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.
Last updated
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)
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.
Worked example and interpretation
A worked example helps translate the vector calculator maths into a realistic scenario so the user can compare the headline result with a concrete set of inputs.
That matters because a result is easier to trust when the page shows how the same logic behaves in a practical case instead of leaving the formula abstract.
Using the result well
Use the vector calculator output as a planning aid, then compare it with the assumptions, units, and caveats shown elsewhere on the page before acting on the number alone.
That extra interpretation step matters because a calculator can simplify the arithmetic but still cannot replace real-world context such as local rules, contract terms, or individual circumstances.
Frequently asked questions
Which operations return a vector vs a scalar?
Addition, subtraction, cross product, and scalar multiplication return vectors. The dot product returns a scalar (a single number).
Why is cross product only for 3D?
The cross product is defined only in three dimensions because it produces a vector perpendicular to both inputs, which requires a third dimension.
How can I check the vector calculator: perform multiple vector operations result manually?
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
Also in Linear Algebra
Related
More from nearby categories
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Vector Addition Calculator
Add multiple 2D or 3D vectors component-wise and find the resultant vector with magnitude.
Vector Subtraction Calculator
Subtract two vectors component-wise in 2D or 3D, with magnitude and step-by-step work.
Dot Product Calculator
Use this dot product calculator to compute the scalar product of 2D or 3D vectors, angle between vectors, cosine similarity, orthogonality, scalar projection.
Cross Product Calculator
Calculate the cross product of two 3D vectors with steps, area, unit normal, right-hand-rule direction, and reversed-order checks.