Why is the magnitude of the sum of two vectors always less than or equal to the sum of both magnitudes?

I know it has something to do with the fact that in vectors we deal with magnitudes and directions, so directions play an important role here.

But I still can't make sense of it. I don't get it. I think this is kind of a philosophical question, but hopefully you'll give me a good answer on that.

Question

Why is the magnitude of the sum of two vectors always less than or equal to the sum of both magnitudes?

I know it has something to do with the fact that in vectors we deal with magnitudes and directions, so directions play an important role here.

But I still can't make sense of it. I don't get it. I think this is kind of a philosophical question, but hopefully you'll give me a good answer on that.

anonymous · Answer

You and your friend have apples. You have 2 apples and your friend has 3 apples. Let assume, you people think that give apples another your friends. There are different combinations. But, we think about extreme situations.  You and your friend eat all apples before give them. So you can not give any apples to your common friend. But, if you do not eat any apples, you can give 5 apples to your common friends. Because of total apples are 5, you can not give 6 apples. Vectors' sum are like that. The result of vectors' sum depend on the angle between them.