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

[oreocookie]

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?

 

[alphysicist]

Hi oreocookie,

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.

 

[baba89]

1. The reason why you cannot always add two numbers with the same dimensions is because dimensions represent different physical quantities. For example, you cannot add 5 meters (length) and 10 seconds (time) together, as they represent different physical quantities. However, you can add 5 meters and 10 meters together, as they have the same units (length). This is because adding numbers with different dimensions does not result in a meaningful physical quantity.

2. No, two nonzero perpendicular vectors cannot be added together to result in a zero vector. This is because perpendicular vectors have different directions and adding them together would result in a diagonal vector, not a zero vector. For example, if you add a force vector pointing north and a force vector pointing east, the resulting vector would have both a north and east component, not a zero component.

3. The question is asking about adding vectors, which is a fundamental concept in physics. Vectors have both magnitude and direction, and they can be added together to find the resultant vector. However, there are certain rules and limitations when adding vectors, such as the two nonzero perpendicular vectors cannot result in a zero vector. It is important to understand these concepts in order to solve more complex physics problems.