What magnitude is not possible when a vector of magnitude 3 is added to a vector of magnitude 4?

choices: a.7 b.0 c.3 d.1 e. 5

I don't think its a. or d.

Any magnitude between 4-3 and 4+3 is possible.

One of your 5 choices is outside that range.

Well, I hope you're sitting down for this mind-boggling revelation - the magnitude that is not possible when a vector of magnitude 3 is added to a vector of magnitude 4 is... *drumroll*... e. 5! Yes, that's right! It's as impossible as finding a unicorn riding a unicycle on a rainbow. So, you can safely eliminate that option from your list without any hesitation. As for a and d, you're right to doubt them. They might be possible in other situations, but not in this particular scenario. So, keep on eliminating and keep on smiling!

To find the magnitude that is not possible when a vector of magnitude 3 is added to a vector of magnitude 4, we can use the triangle inequality.

According to the triangle inequality, the sum of the magnitudes of two vectors must be greater than or equal to the magnitude of their vector sum.

In this case, we have vectors of magnitude 3 and 4, so the sum of their magnitudes must be greater than or equal to the magnitude of their vector sum.

Therefore, the possible magnitudes for the vector sum are:

3 + 4 = 7 (magnitude of 7)
|3 - 4| = 1 (magnitude of 1)

From the given choices, it is evident that option a. (7) and option d. (1) are both possible magnitudes. So, these options can be eliminated.

Therefore, the remaining options are b. (0), c. (3), and e. (5).

To determine the magnitude that is not possible when a vector of magnitude 3 is added to a vector of magnitude 4, we can use vector addition principles. When two vectors are added, their magnitudes can range from the difference between their magnitudes to the sum of their magnitudes.

In this case, we have a vector of magnitude 3 and a vector of magnitude 4. The possible magnitudes of their sum range from 3 - 4 = -1 to 3 + 4 = 7.

Therefore, based on the given choices:
a. 7 is a possible magnitude.
b. 0 is not possible because the sum of two non-zero magnitudes is always non-zero.
c. 3 is a possible magnitude.
d. 1 is possible because 3 - 4 = -1.
e. 5 is possible because 3 + 4 = 7.

So, based on this analysis, the magnitude that is not possible when a vector of magnitude 3 is added to a vector of magnitude 4 is b. 0.