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What is a vector in math?

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Quick answer

In math, a vector is a quantity that has both size (magnitude) and direction — like an arrow pointing a certain way with a certain length. Vectors describe things like velocity and force, where direction matters as much as amount.

Key things to understand

  1. A vector has both magnitude (length) and direction.
  2. It's often drawn as an arrow from one point to another.
  3. Vectors can be added, subtracted, and scaled.
  4. They model real-world quantities like force, velocity, and acceleration.

People also ask

What's the difference between a vector and a scalar?
A scalar has only size (like temperature); a vector has both size and direction (like velocity).
What are vectors used for?
Physics (force, motion), computer graphics, navigation, and machine learning all rely heavily on vectors.
How do you add two vectors?
Place them tip-to-tail and draw an arrow from the start of the first to the tip of the second — that's their sum.