Vectors in three dimensions

Express algebrically and operate with vectors in space

2.

Plot points and vectors in the three-dimensional coordinate system

1.

Three-dimensional coordinate system is system that is used to identify points in space.
When we deal with Three-dimensional space, We add third axis called the Z-axis that passes through the origin and is perpendicular to both the x- and y-axes.

a. (4, 6, 2)

​b. (-2, 4, -5)

Example 2

A tour of the Sierra Madre Mountains lets guests experience nature by zip-lining from one platform to another over the scenic surroundings. Two platforms that are connected by a zip-line are represented by the coordinates (10, 12, 50) and (70, 92, 30), where the coordinates are given in meters.

vectors are i = 〈1, 0, 0〉, j = 〈0, 1, 0〉, and k = 〈0, 0, 1〉

So the i stands for the x-axis, j for the y-axis, and the k is for the z-axis