Component Form of a Vector

Vector Operations

Vector Operations

In Theorem 11.3, u is called a unit vector in the direction of v. The process of multiplying v by to get a unit vector is called normalization of v.

Vector Operations

Coordinates in Space

Figure 11.14

The three-dimensional coordinate system

Distance between points in Space

Distance Formula

Spheres and Midpoints

Equation of sphere

Midpoint Formula

Vectors in Space

Parallel Vectors