Vectors

Add vectors, compute dot and cross products, magnitude and the angle between vectors, with components shown. Try “dot product of (2, −1, 3) and (4, 0, 5)”.

Try an example:

How the Vectors works

  1. Write each vector in component form.
  2. Dot product: multiply matching components and add (2×4 + (−1)×0 + 3×5 = 23).
  3. Use a·b = |a||b|cos θ to find the angle between them.

Frequently asked questions

What does a zero dot product mean?

The vectors are perpendicular (orthogonal).

What is the difference between dot and cross product?

The dot product gives a number (a scalar). The cross product gives a new vector perpendicular to both.

More Geometry & Trigonometry calculators

Geometry CalculatorArea and perimeter of triangles, rectangles, circles and polygons. Volume & Surface AreaCubes, cylinders, cones, spheres and prisms. Pythagorean TheoremFind a missing side of a right triangle. Triangle SolverLaw of sines, law of cosines, angles and sides. Circle CalculatorCircumference, arc, sector, chord and tangent problems. Angles & Parallel LinesAngle sums, polygons, parallel-line and triangle angle rules.

Browse all calculators →

MathMate can make mistakes. Please double-check important steps and calculations.