Vector image on another vector

In summary, the conversation discusses the process of demonstrating an equation of Vector image on another vector (A on B). The main formula is mentioned, and steps are provided. The confusion lies in the use of A and |A|, which are both lengths of the vector A. The person providing the explanation suggests sticking to one notation and not switching between upper and lower case. Eventually, the problem is identified as the incorrect use of the dot product and the need to define the direction when writing the image equation.
  • #1
baby_1
159
15
Hello
I want to demonstrate a equation of Vector image on another vector (A on B)
gif.latex?A_{B}=\frac{(\bar{A}.\bar{B}).\bar{B}}{|B|^{2}}.gif

So i go this steps
gif.gif

and as we know
gif.gif

so change the equation
a}_{B}|Cos\Theta%20_{AB}=\bar{A}.\hat{a}_{B}=|\bar{A}|.\hat{a}_{B}.\hat{a}_{B}=\frac{(A.\bar{B}).gif

but in my equation A is (vector scale) not a (Vector)!
what is my problem?
 
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  • #2
You have [itex]\overline{A}[/itex], [itex]A[/itex], and [itex]\left|\overline{A}\right|[/itex]. I understand that [itex]\overline{A}[/itex] is a vector and that [itex]\left|\overline{A}\right|[/itex] is its length but what is [itex]A[/itex]?
 
  • #3
Thanks for your replay
A and |A| both of them are length of A vector (in electromagnetic books we assume that A=|A| for easy to write)
 
  • #4
Then pick one and stick with it. Similarly, don't swap between upper and lower case.
 
  • #5
I rewrite the Steps.
main formula:
gif.latex?A_{B}=\frac{%28\bar{A}.\bar{B}%29.\bar{B}}{|B|^{2}}.gif


steps:
gif.gif

as we know
gif.gif

and
gif.latex?\bar{A}.gif

so
heta%20_{AB}=\bar{A}.\hat{a}_{B}=|\bar{A}|.\hat{a}_{B}.\hat{a}_{B}=\frac{%28|\bar{A}|.\bar{B}%29.gif


but in my equation |A| is (vector length) not a (Vector)!
what is my problem?
 
  • #6
Oh Baby,

What are you doing? You are taking the dot product of vector A and vector B which results in a scalar. Then you are taking the dot product of that scalar with vector B. That makes no sense.

I think you want the dot product of vector A and vector B/|B|. B/|B| is the unit vector in the B direction.

Ratch
 
  • #7
Thanks friends
i found my probelm
Image of Vector of A on B is a Vector and we should define the direct of it when write the image equation
gif.latex?A_{B}=ACos\Theta%20_{AB}.gif
 

1. What is a vector image?

A vector image is a type of digital graphic that is created using mathematical equations and points instead of pixels. This means that the image can be resized or scaled without losing quality or becoming distorted.

2. What does it mean to have a vector image on another vector?

Having a vector image on another vector means that the two images are layered on top of each other, with the bottom image acting as the background. This allows for more complex and detailed images to be created.

3. How is a vector image on another vector different from a regular image?

Regular images, or raster images, are created using pixels and therefore cannot be resized without losing quality. Vector images, on the other hand, are created using mathematical equations and can be resized without losing quality. Having a vector image on another vector allows for more flexibility and precision in creating detailed images.

4. Can any image be turned into a vector image?

No, only images that are created using mathematical formulas and points can be converted into vector images. Images that are already created using pixels, such as photographs, cannot be turned into vector images.

5. What are some common uses for vector images on another vector?

Vector images on another vector are commonly used in graphic design, logo creation, and animation. They are also used in creating detailed illustrations for websites, product packaging, and marketing materials.

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