Are These Statements About Vectors True or False?

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The discussion centers on two statements regarding vectors. The first statement asserts that the components of a vector remain unchanged regardless of the coordinate system, which is confirmed as true. The second statement claims that the magnitude of the displacement vector from point A to point B can be greater than the actual distance, which is deemed false. The consensus is that the displacement vector's magnitude cannot exceed the distance between the two points. Understanding these concepts is crucial for accurate vector analysis in physics and mathematics.
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1. The components of a vector will be the same no matter what coordinate system is used to express that vector. True or False

2. The magnitude of the displacement vector from A to B can never be less than the distance from A to B, but it can be greater than that distance. True or false

My thoughts:
For question 1 i believe the answer is true just because I don't think the coordinate system changes the vectors. I just want to be sure though by asking other people.

Then for question 2 my gut feeling is false but I really am not to sure about it.
 
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I feel like it is false because I think the displacement vector is the difference between two vectors and it would be impossible to have a greater magnitude than the actual distance. Again though I just want to make sure.Answer:1. True2. False
 

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