Functions
AI Assistant

2D Vectors

Arrows with magnitude and direction — add them, dot them, understand them

A vector has both a magnitude (length) and a direction. On a 2D graph, vectors are arrows from one point to another. The vector \vec{v} = (3, 4) means "go 3 right and 4 up."

You can add vectors tip-to-tail. The dot product tells you how much two vectors point in the same direction — zero when perpendicular.

In this lesson you'll see vectors as labeled segments, add them graphically, compute magnitudes, and explore the dot product.

Graph

FAQ

What is a vector?
A vector has both magnitude and direction. Written as (x, y), it represents a displacement.
How do you find the magnitude?
|\vec{v}| = \sqrt{x^2 + y^2}. For (3, 4): √(9+16) = 5.
How does vector addition work?
Add components: (a_1+b_1, a_2+b_2). Graphically, place tail of b at tip of a.
What is the dot product?
\vec{a} \cdot \vec{b} = a_1 b_1 + a_2 b_2 = |a||b|\cos\theta. Zero means perpendicular.