What magnitude is not possible when a vector of magnitude 3 is added to a vector of magnitude 4?
I'm guessing it depends on the direction of the magnitude.
if both are positive
|3+4|=7
if one is negative
|-3+4|=1
if the other is negative
|3-4|=1
So considering all the possibilities, it can't be anything besides 7 and 1
To determine the magnitudes that are not possible when a vector of magnitude 3 is added to a vector of magnitude 4, we need to consider the possible resulting magnitudes.
When two vectors are added, the resulting magnitude can range from the difference of the magnitudes of the two vectors to the sum of their magnitudes. In this case, the magnitudes of the vectors being added are 3 and 4.
The smallest possible magnitude occurs when the two vectors are antiparallel, meaning they point in exactly opposite directions. In this case, the resulting vector has a magnitude of 4 - 3 = 1. Therefore, the magnitude 1 is possible.
The largest possible magnitude occurs when the two vectors are parallel, meaning they point in exactly the same direction. In this case, the resulting vector has a magnitude of 4 + 3 = 7. Therefore, the magnitude 7 is possible.
Any magnitude between 1 and 7 (inclusive) is also possible, as it is within the range of possible magnitudes when vectors of magnitude 3 and 4 are added.
However, it is important to note that this analysis assumes that the vectors are added tip-to-tail in a straight line. If the vectors are not collinear or are added using other methods (such as the parallelogram method), the resulting magnitudes may differ.