Which of the following principles makes it desirable to calculate a vector sum b

Question

Which of the following principles makes it desirable to calculate a vector sum by breaking the vector into its components?

a. The sum of two vectors pointing in the same direction is in that same direction.

b. The magnitude of the sum of two vectors in the same direction is equal to the sum of the magnitudes of the two vectors.

c. The magnitude of the sum of two vectors in directly opposite directions is equal to the difference of the magnitudes of the two vectors.

d. A vector perpendicular to a given vector has no component in the direction of the given vector.

e. Two of the above are all that are necessary for this to work.

f. All of these together are necessary for this to work.

Need an explanation of the answer. I'm lost with vectors.

Explanation / Answer

Vectors are basically what you have when you provide both a number/magnitude (which people do on a daily basis, everyday experience) along with a direction- wrapped into one quantity. That said, this is a strange question. All of the statements provided are TRUE, but it seems to be asking which ones are relevant to the process of adding vectors when they aren't in the same direction or perpendicular to each other (which are the easiest of situation). When vectors are at odd angles, say one points directly to the right and the other points at 30 degrees from that, it's not as simple as just adding the magnitudes of the vectors. But if you break the individual vectors up into x and components, then add the components, they (components) will all be either in the horizontal or vertical direction, so they'll all be pointing in the same direction or perpendicular, which brings the process back to the simple circumstances described in the options listed. It's hard to tell what your teacher is looking for- this is a poorly written question in my opinion. But my thought would be that you need ALL of the listed statements to be true to make component-adding as simple as it is, otherwise it wouldn't make vector addition much easier. So I'd go with option F.

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