Vector applications

Use vectors to model shapes and movement and interpret lines and planes.

Meaning

Vectors turn position, displacement, parallelism, and perpendicularity into component relationships. Direction vectors describe lines and normal vectors describe planes.

Example

The line from in direction is At it reaches Adding every real multiple of a fixed nonzero direction vector to the base point reaches every position on that line. t=0 is the base point; negative t moves the opposite way. A zero direction vector would not define a line.For a whole line the parameter ranges over all reals. Segments and rays need restricted parameter ranges.

Practice for this concept

Scope and references

Topics

Geometric properties, lines and planes, positions and movement

Learning goal

Use vectors to model shapes and movement and interpret lines and planes.

Helpful background

Choose relevant component or dot-product relationships.