Can some explain vector a+b must be great than a-b

In summary, the conversation discusses the concept of vector addition and subtraction, and whether the statement "vector a+b must be greater than a-b" is true. The participants come to the conclusion that this is not necessarily true, as the magnitude and direction of the resulting vector depends on the angular relationship between the two vectors. They suggest exploring different angles to determine the conditions under which the statement holds true. Additionally, it is noted that this statement is only true for positive scalars, and not in all cases.
  • #1
PoohBah716
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0

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
 
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  • #2
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
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.
 
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  • #3
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

i think one should try checking the contention that addition of two vectors must be greater than subtraction - as it is true in case of scalars.

as vectors are having magnitude as well as direction -their addition and subtraction will result into a vector and its magnitude and direction will depend on the angular relation between them -
suppose the angle between them is 180 degree-then their addition will give you a vector which is smaller than the magnitude of a vector when you subtract one from another.

however if the angle between them is zero their addition will give you a vector larger than the result after taking a difference.
you can try taking an arbitrary angle between them and find the conditions for which the 'contention' holds or does not hold.
 
  • #4
drvrm said:
as it is true in case of scalars.
Is it? Not unless you constrain it to positive scalars...
 
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FAQ: Can some explain vector a+b must be great than a-b

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is commonly represented by an arrow pointing in a specific direction, where the length of the arrow represents the magnitude of the vector.

2. How is vector addition performed?

Vector addition is performed by adding the corresponding components of two vectors. For example, if vector a = (2,3) and vector b = (4,5), then a+b = (2+4, 3+5) = (6,8). The resulting vector represents the combination of the two original vectors.

3. Why must vector a+b be greater than vector a-b?

This is because vector a-b represents the difference between vector a and vector b. If vector a+b is not greater than vector a-b, then it means that vector b is larger than vector a, which would result in a negative vector when subtracted. This does not align with the definition of a vector, which must have a positive magnitude.

4. Can you give an example of vector addition where a+b is greater than a-b?

A simple example would be vector a = (3,4) and vector b = (2,2). When added together, a+b = (3+2, 4+2) = (5,6), which is greater than a-b = (3-2, 4-2) = (1,2).

5. How is vector magnitude related to vector addition?

Vector magnitude is directly related to vector addition, as it determines the length of the resulting vector when two vectors are added together. The magnitude of vector a+b will always be greater than or equal to the magnitude of vector a-b, as the addition of two vectors will always result in a larger vector.

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