 ## Tutoring on Vectors in Space

Learning Objectives:

#### Understand Vectors in Space.

Math Tutoring on Vectors in Space

The xyz-Coordinate System:

We can construct a three-dimensional coordinate system by introducing a third axis called the z-axis. This space is sometimes called R3 in math tutoring. Each point in space is identified by an ordered triple (x, y, z). There are 8 octants rather than 4 quadrants.

The distance between points (x1, y1, z1) and (x2, y2, z2) is given by The midpoint of a line segment with endpoints (x1, y1, z1) and (x2, y2, z2) is given by Vectors in Space:

For a vector with initial point (x1, y1, z1) and terminal point (x2, y2, z2), the Unique Position Vector ‘v’ is The Magnitude or length of ‘v’ is given by The unit vector in the direction of ‘v’ is given by Unit Vectors in Space:

A Unit Vector is a vector with magnitude 1. With Unit Vectors i, j and k any vector in the form can be expressed in the form  Vector Operations in Space:

For vectors and   For Vector and a scalar k: Learn ‘Vectors in Space’ with AffordEdu.

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Hook Questions:

1.     What is the xyz-Coordinate system?

2.     Find the magnitude of a Vector in Space and Unit Vector in Space?

3.     Deduce various Vector Operations in Space.

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