Vector basic problem

1. Oct 8, 2017

Mathematicsss

Mod note: Moved to Precalc section
1. The problem statement, all variables and given/known data
Find the midpoint of the vector AB

A(3,2,5) B(1,3,2)

2. Relevant equations
Not sure

3. The attempt at a solution
I wrote each point in terms of the unit vectors, i,j,k then I subtracted the two, and divided by a 2.

Last edited by a moderator: Oct 8, 2017
2. Oct 8, 2017

Orodruin

Staff Emeritus
In the future, please do not just describe what you did. Show us what you did and what result you got.

Now. Why did you take the difference and divide by two? Why do you think that will give you the midpoint? If you think just about real numbers, say 4 and 10, which number is the midpoint between those and do you get it by taking (10-4)/2?

3. Oct 8, 2017

Mathematicsss

Because vector AB is point B relative to A, and so I subtracted the two to find the new point, and then wrote the new point in the form of i,j and k unit vectors. I then divided in order to the midpoint of the the new vector. However, I am not sure why it is that it doesn't work with the numbers you wrote (4 and 10), can you please explain?

4. Oct 8, 2017

Orodruin

Staff Emeritus
This gives you the difference vector between A and B, not the midpoint. Consider the case when A and B are the same point, you would get zero.

What would you do to mathematically find the midpoint between 4 and 10?
Edit: It is obviously 7, but how do you reach this conclusion?

5. Oct 8, 2017

Mathematicsss

To find the midpoint between 4 and 10, I add 4+10 and divide by 2.

6. Oct 8, 2017

Orodruin

Staff Emeritus
So why are you not doing the same for your problem?

7. Oct 8, 2017

Oh, I see.

8. Oct 8, 2017

Mathematicsss

I have another question, to write A(3,2,5) as a position vector, it would be 3i+2j+5k correct?

9. Oct 8, 2017

Orodruin

Staff Emeritus
Assuming that the (3,2,5) are the Cartesian coordinates, yes.

10. Oct 8, 2017

Mathematicsss

What if I was asked just to find the position vector AB?

11. Oct 8, 2017

Orodruin

Staff Emeritus
AB is not a position vector, it is a difference vector.

12. Oct 8, 2017

Mathematicsss

Yes, I know.. I meant that what if we were supposed to find a position vector, AB, is that possible? and what if I wrote AB (difference vector) in the form of I,j, and k? wouldn't it be a position vector? Assuming A and B are cartesian coordinates?

13. Oct 8, 2017

Orodruin

Staff Emeritus
No. It would only be a vector. The only thing that is a position vector is the vector from the origin to a given point. AB is not such a vector.

14. Oct 8, 2017

Mathematicsss

Alright, do you suggest that in order for myself to solve vector problems that are in R^3, it would be helpful to use an analogy in R^2?

15. Oct 8, 2017

Mathematicsss

last two questions, 1)if I added the two vectors are wrote them in I,j,and k, will I get a position vector?
2) Will there ever be a case where I will not be able to find the midpoint of AB?

Thank you very much, you have been very helpful. I apologise for taking much of your time. Have an amazing day!

16. Oct 8, 2017

FactChecker

We need to be careful of the wording of the question. As stated, I think that the vector AB is (-1, 1/2, -3/2). That is the vector originating at (0,0,0). The vector from A to B is exactly the difference as stated in the OP and the midpoint of that vector is obtained as stated in the OP.

If the problem had asked for the midpoint of the line from A to B, I think that would be different. That would be (A+B)/2. Or if the question had asked for the vector from the origin to the midpoint between A and B, that would also be the vector from the origin to the point (A+B)/2 = A + (AB/2)

PS. I'm using bold to indicate vectors because I have never been able to consistently get the vector symbol to work.

17. Oct 8, 2017

Orodruin

Staff Emeritus
I don't think the question in the OP is very well worded. I suspect it might not be stated exactly as given.

In my mind it does not make sense to ask for the "midpoint" of a vector. You only ask for the midpoint between to given points. If I wanted half the distance vector between the points, I would ask for half of AB. I suspect the problem might have come with a figure indicating AB as the vector from A to B. In that case, the midpoint of the vector would indeed be the midpoint between A and B. Without further specification and the problem stated exactly as given, we simply do not know.

18. Oct 8, 2017

FactChecker

I agree.
Good point.
I agree. It's unfortunate that the wording is so treacherous.

19. Oct 8, 2017

LCKurtz

Try $\vec A$. It will render as $\vec A$.

20. Oct 9, 2017

FactChecker

Thanks. After some experimenting, I see that it was when I tried to use a bold letter as a vector that it didn't work for me:
Not bold: $\vec A$
Bold: $\vec A$