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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]
Nick89 said:Don't forget what a vector is!
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.
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.
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.
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.
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.