2D & 3D Vector Calculator
Compute vector sums, differences, magnitudes, dot products, unit direction vectors, and angles in 2D and 3D space.
Vector A (u)
Vector B (v)
What is a Vector?
In physics and linear algebra, a vector is a mathematical quantity possessing both magnitude (length) and direction. They represent physical phenomena such as velocity, force, acceleration, and momentum.
Frequently Asked Questions
How is vector magnitude calculated?
The magnitude of a 3D vector V = (x, y, z) is determined by the 3D Pythagorean theorem: |V| = √(x² + y² + z²).
What does a dot product of zero mean?
When two non-zero vectors have a dot product of zero, they are strictly orthogonal (perpendicular to each other at 90 degrees).
How do you find the angle between two vectors?
The angle θ between two vectors is given by θ = arccos[(A · B) / (|A| |B|)].