Is Scalar Addition Equivalent to Adding Parallel Vectors?

[Tiven white]

Homework Statement

T/F: The addition of two scalars is equivalent to the addition of parallel vectors.
Select one:
a. False
b. True

Homework Equations

The Attempt at a Solution

i said true reason being the magnitude of vectors can be added if they are in the same direction by tail to tip method.
is this correct?

 

[PhanthomJay]

I wouldn't say so. Although the magnitudes may be the same, vector addition still has direction, scalars ahve none. What if the parallel vectors are in opposite directions?

 

[jackarms]

I'd say it's true. I think by "equivalent" it means that the two are just analagous, so for scalars you just add the magnitudes, and for parallel vectors you also just add the magnitudes. I think by "parallel" it implies that they are both in the same direction, instead of being anti-parallel.

 

[PhanthomJay]

I'd say it's true. I think by "equivalent" it means that the two are just analagous, so for scalars you just add the magnitudes, and for parallel vectors you also just add the magnitudes. I think by "parallel" it implies that they are both in the same direction, instead of being anti-parallel.

Maybe yes. But we have to guess what is meant by 'equivalent' and to a certain extent, 'parallel' vectors. I think the question needs to be tossed in the trash.

 

[HalfLostAndSearching]

Your response is partially correct. The statement is true, but your reasoning is not entirely accurate. The addition of two scalars is equivalent to the addition of parallel vectors because scalars have magnitude but no direction, while vectors have both magnitude and direction. Therefore, when adding two scalars, the result will only have a magnitude and no direction, which is the same as adding parallel vectors. However, this only applies to parallel vectors, not all vectors. If the vectors are not parallel, their addition will result in a vector with both magnitude and direction. So, the statement is true, but your reasoning needs to be clarified.