The Vector Cross Product
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Transcript of The Vector Cross Product
DefinitionThe cross product of two 3-d vectors becomes a 3-d vector itself.The cross product is:
An easier method is to use the formula listed in the matrices part of the formula sheet.
Example
Method 1
Method 2
Applications of vxw - the perpendicular vectorThe resulting vector of the cross product of vxw will always be
perpendicular to v and w, as shown in the diagram below.Find the vector that is perpendicular to:
1. and
2. 3i + 2j - k and 3j - 5k.
-7i + 15j + 9k
Applications of vxw - the area of a triangle or parallelogram
Area of a triangle is given by . If a and b are vectors the area of a triangle becomes:
Expand and simplify
Proof:
Find the area of the triangle with vertices A(1,1,2) B(-1,3,2) and C(4,1,5).
Find two sides of the triangle, the vectors AB and AC.
and
Now find the cross product of the two vectors:
The area is given as follows: