# What happened to the magnitude of a vector when it is divided by a positive number?

(a) it increases

(b) it decrease

(c) it remains same

Kindly explain

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• (a) it increases or

(b) it decreases or

(c) it remains the same

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• It is a dichotomy. No single correct answer. It is conditional on the positive Number </> 1.

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• A couple of answers point out that this question has no correct answer for an arbitrary vector. Just as in ordinary multiplication, division by 0.5 is the same and multiplication by 2, and vice versa.

However, if you interpret the question as implying a guarantee that one of those answers is indeed correct, then you get an interesting conclusion: The only way for one of those answers to be correct for all x>0 is for the vector to be the zero vector!

Division of a vector by a real number is defined as multiplication of the vector by the reciprocal of that real number. Multiplying the zero vector by any number gives the zero vector as a product. So, if I had to pick an answer to this question, I'd choose "(c) it remains the same".

That sort of "trick question" thinking is probably better left to solving "brain teaser" type puzzles. In a serious math course, the conditions ought to be clearly spelled out.

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• unknown. If the positive number is >1 then it decreases

If the positive number is < 1 then it increases

If the positive number = 1 then it doesn't change

If the positive number = 0 then it is indeterminent

explain? try a few examples.

100 / 2 = 50, which is <100

100/0.5 = 200, which is >100

I suspect perhaps you mean "divided by a positive integer" ? but that is still unknown, since 0 and 1 are positive integers.

• neb
Lv 7
6 months agoReport

I don’t think zero is considered a positive integer.

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• Hello,

The correct answer isn't "it increases", "it decrease" or "it remains same".

IT DEPENDS.

It depends on the positive value:

- If it is LESS THAN 1, the magnitude will INCREASE.

- If it is EQUAL TO 1, the magnitude will STAY THE SAME.

- If it is GREATER THAN 1, the magnitude will DECREASE.

Dividing a vector by a positive number merely divides its magnitude by that same positive number.

So:

2 / 0.5 = 4 ← Increase

2 / 1 = 2 ← Stay the same

2 / 2 = 1 ← Decrease

Explicatively,

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