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:
What you can do with the Vectors
Add, dot product, cross product, magnitude and angle between vectors.
Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.
Example input
e.g. dot product of (2, -1, 3) and (4, 0, 5)
How the Vectors works
- Write each vector in component form.
- Dot product: multiply matching components and add (2×4 + (−1)×0 + 3×5 = 23).
- 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.
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Math Solver can make mistakes. Please double-check important steps and calculations.