Vectors in Space

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:

 

 

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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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