Solved: R Vectors in Different Drawings Same Magnitude?

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In summary, the resultant vector of A + B - C is the same in both drawings because vector addition is commutative and the order of the vectors does not matter. This can be confirmed by assigning simple numbers to the variables.
  • #1
razored
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[SOLVED] Is the R the same?

Question : Is the resultant vector of A + B - C the same magnitude in both drawings? I rearranged the vectors to form a different shape, but they would still have the same resultant vector, right?

http://img150.imageshack.us/img150/826/38838600id4.gif
 
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  • #2
Yes, because essentially what you are doing in the first drawing is A + B + (-C), whereas in the second drawing you have B + (-C) + A.

This is perfectly fine since vector addition is commutative (it doesn't matter what order the vectors are added in).
 
  • #3
Easy way to check is assign simple numbers to your variables.
 
  • #4
Thank you for the quick and accurate results.
 

1. What are R vectors and how do they differ in different drawings?

R vectors are mathematical objects that represent both direction and magnitude. In different drawings, they can differ in terms of their direction, orientation, and starting point, but they will have the same magnitude.

2. How can I determine if two R vectors in different drawings have the same magnitude?

You can determine if two R vectors have the same magnitude by using the Pythagorean theorem. If the length of both vectors are equal, then they have the same magnitude.

3. Can R vectors in different drawings have the same magnitude but different direction?

Yes, R vectors in different drawings can have the same magnitude but different direction. This is because the magnitude of a vector only represents its length and not its direction.

4. Why is it important to understand R vectors in different drawings with the same magnitude?

Understanding R vectors in different drawings with the same magnitude is important because it helps us to understand the concept of vector equivalence. This concept is crucial in various fields of science, such as physics and engineering, where vector quantities play a significant role.

5. What are some real-world applications of R vectors in different drawings with the same magnitude?

R vectors in different drawings with the same magnitude have many real-world applications. They are used in navigation systems, such as GPS, to determine direction and distance, and in physics to calculate forces and velocities. They are also used in computer graphics and animation to create realistic movements.

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