Help with physics demonstration

In summary, the conversation is about a demonstration involving different values for a and the equations a x b = a x c and a.b = a.c. The hint suggests crossing both sides of the first equation with a, but the result is 0=0. The conversation then shifts to clarifying the definitions of the dot and cross product, with the clarification that "a x b" means a cross product with b and "a.b" means a dot product. The conversation ends with a discussion about the definitions of the dot and cross product, with an example of (1,2) x (3,4) and (1,2).(3,4) and a demonstration that the desired result cannot be proven with just vector multiplication
  • #1
brad sue
281
0
Hi ,
Please can I have some help with this demonstration:
Let a#0 ( #= different)
Show that if a x b = a x c and a.b=a.c, then b=c ( Hint: Cross both sides of the first equation with a)
When I cross by a ( as the hint suggests) , I found 0=0 ??
thank you
 
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  • #2
What is "a x b" vs. "a.b"?
 
  • #3
What are your definitions of The dot and cross product?
 
  • #4
Integral said:
What are your definitions of The dot and cross product?
Hi , I don't know what you mean but I guess you want to know that
"a x b" means a cross product with b
and
"a.b" mean a dot b
Thank you
B
 
  • #5
brad sue said:
Hi , I don't know what you mean but I guess you want to know that
"a x b" means a cross product with b
and
"a.b" mean a dot b
Thank you
B
Right. So, is "dot" vector multiplication? How is "cross product" different than vector multiplication? Some examples would be useful. What is (1,2) x (3,4)? What is (1,2).(3,4)?
Let's say a, b, and c are vectors. Let a=(1,2), b=(1,2) and c=(c1,c2).
ab = ac ---> a1b1 + a2b2 = a1c1 + a2c2 ---> 5 = c1 + 2 c2 ---> c1 = 5 - 2 c2, which means that although c = (1,2) would satisfy the equation, so would c = (5,0). Therefore what you want to demonstrate is not demonstrable on the basis of vector multiplication alone. That is why more info is needed on the exact definitions of the cross and the dot.

My guess is they are inner and outer products: a.b = a1b1 + a2b2, axb = (a1b1, a1b2, a2b1, a2b2). But can you verify this so we won't be making a mistake?
 
Last edited:

FAQ: Help with physics demonstration

What are some tips for creating a successful physics demonstration?

When creating a physics demonstration, it is important to keep the following tips in mind:

  • Choose a topic that is interesting and relevant to your audience.
  • Make sure the materials and equipment are easily accessible and safe to use.
  • Practice the demonstration beforehand to ensure its effectiveness.
  • Explain the scientific principles behind the demonstration to educate and engage your audience.
  • Be prepared for unexpected outcomes or questions from your audience.

How can I make my physics demonstration interactive?

There are several ways to make your physics demonstration interactive:

  • Include audience participation by asking for volunteers or having them make predictions about the outcome.
  • Use props or visuals to engage the audience's senses.
  • Encourage questions and discussion during and after the demonstration.
  • Incorporate hands-on activities or experiments for the audience to try themselves.
  • Include elements of surprise or humor to keep the audience engaged.

What are some common mistakes to avoid when creating a physics demonstration?

Some common mistakes to avoid when creating a physics demonstration include:

  • Using materials or equipment that are unsafe or not appropriate for the audience.
  • Not practicing the demonstration beforehand, leading to unexpected outcomes or technical difficulties.
  • Not explaining the scientific principles behind the demonstration clearly or in a way that is easy for the audience to understand.
  • Not considering the age or level of understanding of the audience when choosing a topic.
  • Not being prepared for questions or unexpected outcomes during the demonstration.

How can I incorporate technology into my physics demonstration?

There are many ways to incorporate technology into a physics demonstration:

  • Use a projector or interactive whiteboard to display visuals or simulations.
  • Use sensors or data collection devices to measure and display data in real-time.
  • Use video or audio recordings to enhance the demonstration or provide additional information.
  • Utilize online resources or apps to supplement the demonstration or provide interactive elements.
  • Use social media or online platforms to engage with the audience before or after the demonstration.

How can I ensure that my physics demonstration is accessible to all audience members?

To ensure that your physics demonstration is accessible to all audience members, consider the following:

  • Choose a topic that is relevant and interesting to a diverse audience.
  • Provide alternative materials or equipment for individuals with disabilities.
  • Use visuals or props that are easily visible to those with visual impairments.
  • Include captioning or sign language interpretation for individuals with hearing impairments.
  • Be mindful of any potential triggers for individuals with sensory sensitivities.

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