(a) Define vector product (b) Understand the properties of vector product (c)Find the area of parallelogram

Definition of The Vector Product (or Cross Product) then the vector product, denoted by is defined in terms of the expansion of the symbolic determinant as follows : If and

Geometrically, if where is the angle between is a unit vector in the direction perpendicular to the plane containing andand is defined as

To determine the direction of use the right-hand rule, where the fingers turn from to and the thumb points in the direction of

By referring to the above diagram, we note that

Example 1 Hence prove thatis perpendicular to the vector

Solution

From the previous lesson, we know that is perpendicular to

The properties of Vector Product

AB C D

Example 2 Solution

Example 3

Solution

Example 4

Solution

(b) A D CB ( the position vector of D)

A D CB

CONCLUSION 1. The Vector Product (Or Cross Product) 2. The Angle Between Two Vectors 3. The Area of a parallelogram if given 2 side vectors