Solving Homework Equations Involving A & B

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In summary, the two parts of the problem are unrelated and should be approached separately. In part A, it is known that the angle between A and B is 120 degrees or 240 degrees, but more information about the vectors cannot be determined from this. In part B, the components of B can be found using the scalar/dot product of A and B, which is AxBx + AyBy. The solution to part A does not help in solving part B, but by comparing the equations A*B = 5Ay-7Ax and A*B = AxBx + AyBy, it can be determined that B-C = 5Ay-7Ax, which can help in finding the components of B.
  • #1
student 1
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Homework Statement


A. If A*B=-(1/2)AB, what do you know about A and B.
B. If A*B=5Ay-7Ax, find B.


Homework Equations





The Attempt at a Solution


Part A I know the angle is 120 degrees in between A and B. Would I know more about the two vectors from that?
Part B. I don't know where to begin to try and answer that?
 
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  • #2
For A, it could be also be 240 degrees.

For B, think in terms of the components of the vectors. How do you represent a scalar/dot product of two vectors in terms of their components?
 
  • #3
AxBx+AyBy with that I should be able to find my B?
 
  • #4
Yes.
 
  • #5
Do I use what I know in the first part of the problem as well or would this be a totally different scenario??
 
  • #6
student 1 said:
Do I use what I know in the first part of the problem as well or would this be a totally different scenario??
A better question that you must ask yourself should be, does the the answer to the first problem help you in anyway in solving the second, given that you know component-wise multiplication of vectors?
 
  • #7
So Bx and By would simply be 1 since they are not in the problem right?
 
  • #8
Of course not.You have to solve in the context of the upper question.
 
  • #9
According to the teacher part A and B are unrelated, they are two separate problems, in that case bx and by would be 1 correct?
 
  • #10
Part B tells you that A*B=5Ay-7Ax. And, of course, A*B= AxBx+ AyBy. Just compare those two equations!
 
  • #11
student 1 said:
B. If A*B=5Ay-7Ax, find B.

Hi student 1! :smile:

(have you noticed the new X2 and X2 tags? :biggrin:)

Hint: If 5Ay - 7Ax = A.C also, what can you say about B - C? :wink:
 

1. What is the first step in solving homework equations involving A and B?

The first step in solving homework equations involving A and B is to identify the variables A and B and determine which one is the independent variable (the one that can be changed) and which one is the dependent variable (the one that is affected by the change in the independent variable).

2. How do I know which equation to use for a specific problem involving A and B?

In order to determine which equation to use, you need to carefully read the problem and identify which variables are given and which ones you are trying to find. Then, you can use your knowledge of algebra and mathematical principles to select the appropriate equation to solve the problem.

3. Can I use the same equation for different problems involving A and B?

Yes, you can use the same equation for different problems involving A and B as long as the variables and conditions are the same. However, if there are any changes in the variables or conditions, you may need to use a different equation or adjust the one you are using accordingly.

4. How do I check if my solution to a homework equation involving A and B is correct?

You can check your solution by plugging in the values of A and B into the original equation and solving for the dependent variable. If the result matches the value you were trying to find, then your solution is correct. You can also double check your work by solving the equation using a different method or using a calculator.

5. What should I do if I am stuck on a homework equation involving A and B?

If you are stuck on a homework equation involving A and B, it is important to first make sure you understand the problem and have all the necessary information. If you are still struggling, you can try breaking the problem down into smaller parts or seeking help from your teacher or peers. Additionally, there are many online resources and tutorials available that can provide guidance and examples for solving equations involving A and B.

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