Dot product of vector function?

In summary, the conversation discusses finding the angle between two functions by turning them into vector valued functions and finding the dot product at a given variable value. There is a discussion about the limitations and advantages of this method, and the concept of a vector as a function on a finite set is brought up.
  • #1
lewis198
96
0
Greetings.

I was thinking about finding the angle between two functions, so I thought it may be elegant to turn them into vector valued functions, and find the dot product at a given variable value where the vectors lie on the same plane and are functions of the same variable. I'm going to go away and try it, but what do you guys think about this?

What are the limitations of this method, and/or the advantages?
Thanks guys.
 
Last edited:
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  • #2
What do you mean by "the angle between two functions"? Do you mean the angle between the tangent lines to their graphs at a point of intersection?
 
  • #3
lewis198 said:
Greetings.

I was thinking about finding the angle between two functions, so I thought it may be elegant to turn them into vector valued functions, and find the dot product at a given variable value where the vectors lie on the same plane and are functions of the same variable. I'm going to go away and try it, but what do you guys think about this?

What are the limitations of this method, and/or the advantages?
Thanks guys.

the angle between two functions is well defined if the functions are square integrable.

you can think of a vector as a function on a finite set so there is really no conceptual difference between a function and a vector.
 

Related to Dot product of vector function?

1. What is the dot product of a vector function?

The dot product of a vector function is a mathematical operation that takes two vectors and produces a scalar value. It is also known as the inner product or scalar product.

2. How is the dot product of a vector function calculated?

The dot product of a vector function is calculated by taking the sum of the products of the corresponding components of the two vectors. This can be written as a formula: A · B = |A| x |B| x cosθ, where |A| and |B| are the magnitudes of the two vectors and θ is the angle between them.

3. What is the significance of the dot product in vector calculus?

The dot product has several important applications in vector calculus. It can be used to calculate the angle between two vectors, determine if two vectors are perpendicular, and find the projection of one vector onto another.

4. How is the dot product related to the magnitude of a vector?

The dot product is related to the magnitude of a vector through the formula A · A = |A|^2. This means that the dot product of a vector with itself is equal to the square of its magnitude.

5. Can the dot product of vector function be negative?

Yes, the dot product of a vector function can be negative. This occurs when the angle between the two vectors is greater than 90 degrees. In this case, the dot product is negative and represents the opposite direction of the vector being multiplied.

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