2 min read•Last Updated on July 25, 2024
Vector-valued functions take us beyond single values, outputting vectors instead. They're like a GPS for math, giving us x, y, and z coordinates all at once. These functions help us map out paths in 3D space, tracing curves like helixes and circles.
Graphing these functions is like connecting the dots in three dimensions. We plot points, figure out which way the curve's going, and join them up. The domain tells us what inputs work, while the range shows all possible outputs. It's like setting the boundaries for our mathematical playground.
Term 1 of 16
A circle in 3D space is a set of points that are equidistant from a given point, called the center, and lies on a plane. This concept expands the traditional idea of a circle from a 2D plane to three dimensions, where the circle can be oriented in any direction and can have various positions relative to the coordinate axes. Understanding circles in 3D involves using vector-valued functions to describe their location and movement within that space.
Term 1 of 16
A circle in 3D space is a set of points that are equidistant from a given point, called the center, and lies on a plane. This concept expands the traditional idea of a circle from a 2D plane to three dimensions, where the circle can be oriented in any direction and can have various positions relative to the coordinate axes. Understanding circles in 3D involves using vector-valued functions to describe their location and movement within that space.
Term 1 of 16
A circle in 3D space is a set of points that are equidistant from a given point, called the center, and lies on a plane. This concept expands the traditional idea of a circle from a 2D plane to three dimensions, where the circle can be oriented in any direction and can have various positions relative to the coordinate axes. Understanding circles in 3D involves using vector-valued functions to describe their location and movement within that space.