Learning Objectives:

__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 **R ^{3}** in math tutoring. Each point in space is identified by an ordered triple

The distance between points **(x _{1}, y_{1}, z_{1})** and

The midpoint of a line segment with endpoints **(x _{1}, y_{1}, z_{1})** and

* *

*Vectors in Space:*

For a vector with initial point **(x _{1}, y_{1}, z_{1})** and terminal point

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.**

Interested in free assessment? Build your personalized study plan with AffordEdu through knowledge map and go for free assessment and free tuition session with math expert.*

** **

**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.*

** **

**Learn ‘Vectors in Space’ with AffordEdu Online One on One Math Tutoring.**

** **

Struggling with **Vectors in Space**?** **Need math help for homework? You are not the only one. Fortunately, our expert tutors in math tutoring** **are online now and are ready to help.