The sum of two vectors has the greatest magnitude when the angle between these two vectors is?
What angle between two vectors results in the maximum magnitude of their sum?
8 Answers
When you add vectors, anytime there is an angle you have to multiply by some cosine, which always has a value between 0 and 1. So anytime you use trig, your going to reduce your value, usless your result is 1 for the trig portion.
cos(0)=1
This means that you want no angle difference to get the max magnitude result. so when you add to vectors with a zero degree angle difference your going to get the most out of the result.
another way to look at it is to travel the two vectors. if you traveled in any pattern other then a straight line you would be wasting distance, so any corners or "angles" that you turn means that you have traveled a less efficient way to your final destination.
of course zero degrees or a factor of 360 degrees that is n*360 , where n=0,1,2.... . that's when the two vectors will work in the same direction & their magnitudes will add up.
they have the least magnitude when the two vectors are 180 degrees apart. this is the position in which the two vectors will act contrary to each other hence their magnitudes will be substracted.
When they act parallel and in the same direction, meaning 0º between each other.
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