Finding A and B to Satisfy A X B = B

  • Thread starter student 1
  • Start date
In summary, the conversation discusses solving for A and B in the equation A x B = B, with the additional information that A=Axi+Ayj and A x B = Ayi-Axj. The conversation also mentions the formula |A x B| = |A| |B| sin theta and reminds the student of the definition of a vector. The solution involves understanding the relationship between A, B, and the resulting vector C.
  • #1
student 1
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Homework Statement


Can A X B = B? If so, find A, and illustrate with a picture
B. If A=Axi+Ayj, find B such that A X B = Ayi-Axj


Homework Equations


I know A X B= ABsin[tex]\theta[/tex]


The Attempt at a Solution

 
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  • #2
You have missed the important part:

The Attempt at a Solution



Show some work, we won't simply give you the answers here!

I will give you one hint though. The expression you gave (AxB = ABsin..) is technically not correct.
The correct expression is:
[tex]\left| \vec{A} \times \vec{B} \right| = \left| \vec{A} \right| \left| \vec{B} \right| \sin \theta[/tex]

In other words, it only gives you the length of the vector. Don't forget what a vector is!
 
  • #3
Well i just need to know how to begin. I know If A is only in the x,y plane and B is only in the x,y plane then there's no way that's possible. However i don't know how to determine it with 3 different axis.
 
  • #4
Nick89 said:
Don't forget what a vector is!

Student1, a vector is something with a magnitude and a direction.
 
  • #5
If you have:
[tex]\vec{A} \times \vec{B} = \vec{C}[/tex],
what do you know about the vector C in relation to A and B?
 

1. How do you find A and B to satisfy the equation A X B = B?

The key to finding A and B to satisfy the equation A X B = B is to understand that the solution will depend on the values of A and B. One approach is to substitute different values for A and B and solve for the other variable until the equation is satisfied. Another approach is to use algebraic manipulation to rearrange the equation and solve for A or B.

2. Can you give an example of A and B that satisfy the equation A X B = B?

Yes, for example, let A = 2 and B = 4. When we substitute these values into the equation, we get 2 X 4 = 4, which is a true statement. Therefore, A = 2 and B = 4 satisfy the equation A X B = B.

3. Is there only one solution for A and B in the equation A X B = B?

No, there are infinitely many solutions for A and B in the equation A X B = B. This is because for any value of A, we can find a corresponding value of B that satisfies the equation. For example, if A = 3, then B = 3 also satisfies the equation, as well as any other value of B that is equal to 3.

4. What are some real-life applications of the equation A X B = B?

The equation A X B = B is commonly used in mathematics and science, but it also has practical applications in everyday life. For example, it can be used to calculate discounts when shopping (where A represents the original price and B represents the discount percentage), determine the final amount in a savings account after interest (where A represents the initial amount and B represents the interest rate), or even calculate the total number of combinations in a lock with A possible numbers on each dial and B total dials.

5. Can the equation A X B = B have negative solutions for A and B?

Yes, the equation A X B = B can have negative solutions for A and B. This can happen when either A or B (or both) are negative numbers. For example, if A = -2 and B = -5, when we substitute these values into the equation, we get (-2) X (-5) = -5, which is a true statement. Therefore, A = -2 and B = -5 satisfy the equation A X B = B.

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