The discussion centers on the assertion that the vector sum \( \mathbf{a} + \mathbf{b} \) must be greater than the vector difference \( \mathbf{a} - \mathbf{b} \). Participants conclude that this statement is not universally true, as the relationship between the vectors depends on their magnitudes and the angle between them. Specifically, if the angle between vectors \( \mathbf{a} \) and \( \mathbf{b} \) is 180 degrees, the magnitude of \( \mathbf{a} + \mathbf{b} \) can be less than that of \( \mathbf{a} - \mathbf{b} \). Thus, constraints on the vectors are necessary for the statement to hold.
PREREQUISITESStudents of physics and mathematics, particularly those studying vector calculus, as well as educators seeking to clarify misconceptions about vector operations.
It is certainly not true in general (not even for scalars). You would need to constrain a and b more to have something that was true.PoohBah716 said:Homework Statement
Can some explain vector a+b must be great than a-b
Homework Equations
none this is conceptual
The Attempt at a Solution
I believe this is false because the direction can be + or -. can you explain to your thoughts
PoohBah716 said:Can some explain vector a+b must be great than a-b
Homework Equations
none this is conceptual
The Attempt at a Solution
I believe this is false because the direction can be + or -. can you explain to your thoughts
Is it? Not unless you constrain it to positive scalars...drvrm said:as it is true in case of scalars.