Vectors
Free lessons and practice worksheets for vectors — worked examples, common mistakes, and step-by-step solutions.
- 01Vectors3 min read
Vectors
Advanced 3D vectors extend basic vector operations into three-dimensional space, incorporating x, y, and z components. These vectors support operations like dot products, cross products, and parametric equations that describe lines and planes in 3D coordinate systems. The cross product uniquely produces a vector perpendicular to both input vectors, while the dot product yields a scalar measuring alignment between vectors.
- 02Vectors3 min read
Vectors
A vector in two dimensions represents both magnitude (length) and direction, written as an ordered pair (x, y) where x and y are the horizontal and vertical components. Unlike a scalar quantity such as temperature or speed, a vector contains directional information that makes it essential for describing motion, forces, and position changes. The vector from point A(-3, 1) to point B(4, 6) is written as (7, 5), found by subtracting the starting coordinates from the ending coordinates.