Why Can't You Always Add Numbers with the Same Dimensions?

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Adding numbers requires them to have the same units, but having the same dimensions does not guarantee they can be added. For example, adding length to time is dimensionally incorrect, even though both are measurable quantities. Additionally, two nonzero perpendicular vectors cannot sum to zero, as their resultant will always have a magnitude equal to the square root of the sum of their squares. Clarification on the questions is needed for better understanding. Understanding the distinction between units and dimensions is crucial for solving these types of problems.
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Homework Equations


1. You can always add two numbers that have the same units. HOwever, you cannot always add two numbers that have the same dimensions. Explain why not, and include an example in your explanation.
2. Can two nonzero perpendicular vectors be added together so their sum is zero? Explain.


3. I'm not really sure what the question is asking me. Can someone help?
 
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Hi oreocookie,

oreocookie said:

Homework Equations


1. You can always add two numbers that have the same units. HOwever, you cannot always add two numbers that have the same dimensions. Explain why not, and include an example in your explanation.
2. Can two nonzero perpendicular vectors be added together so their sum is zero? Explain.


3. I'm not really sure what the question is asking me. Can someone help?

Please post your thoughts on these questions, and then we'll know how to help.
 

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