Dot Product (Projection) - Maple Programming Help

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Dot Product (Projection)

Main Concept

Given two vectors  a and b, their dot product is the scalar quantity

 

a  b = a|b|cosθ

where θ is the angle between a and b.

 

The dot product can also be expressed in terms of the components of a and b as follows:

 

ab = a1b1 + a2 b2 +a3 b3

 

The unit vector in the direction of  a is given by

a^=aa

 

The vector projection of  a on b is the orthogonal projection of a onto the line in the direction of b:

 

 acosθb^ = ab^b^ =ab b b2= axbx + ay by + azbzbx2+ by2 +by2  b 

 

The scalar projection of  a on b is the length of the associated vector projection.

 

acosθ = ab^ =ab |b| = axbx + ay by + azbzbx2+ by2 +by2

 

Click and or drag on the graph to change the two vectors. See how they affect the scalar and vector projections.

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