# Vectors (Magnitude)

1. ### FeDeX_LaTeX

434
Hello;

1. The problem statement, all variables and given/known data
"The point C lies between A and B and is 5 units from A.

OA = 2i + 3j
OB = -4i - 5j

Find OC."

2. Relevant equations
Pythagoras' Theorem

3. The attempt at a solution
This is not exactly a homework question since this is independent study, but I was wondering why I couldn't get the same answer as my textbook unless my textbook is wrong - but if it isn't, then that means I haven't grasped this topic yet.

First find the vector AB;

AB = OB - OA
AB = -4i - 5j - 2i - 3j = -6i - 8j

The magnitude of AB is therefore 10, by Pythagoras' Theorem.

Since C is 5 units from A and lies between A and B;

AC = (AB)/2

AC = 0.5(-6i - 8j) = -3i - 4j

To find OC, we simply substitute values into the equation OA + AC = OC;

OA + AC = OC
2i + 3j - 3i - 4j = -i - j = OC

So OC should be -i - j, but I don't see the error I have made... my textbook says it should be 0.8i + 1.4j. This problem has been bugging me because I thought I understood this, perhaps there is something deeper I haven't noticed/considered?

Thanks.

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3. ### tiny-tim

26,043
Hello FeDeX_LaTeX!

Your method looks correct to me.

Perhaps the question should say 2 units instead of 5 ?

4. ### FeDeX_LaTeX

434
Hello;

Thank you for the quick reply!

I did the problem again assuming it was 2 units from A, not 5, and I did indeed get the textbook's answer. But the problem does say 5 units. I suppose it is just a typo.

Thanks! Now just one more topic and I've finished this chapter.