First time posting Need extreme help on vectors

[Skatehabitat2]

I want to first say hello to everybody and thank you for this site because it is great and I have only been looking at it for about 2 hours. I need big time help in physics, but I am very interested in it so I guarantee I will be back very often and I hope it is not a problem to post/answer questions very often

Homework Statement

A jogger travels a route that has two parts. The first is a displacement A of 2.50 km due south and the second involves displacement B that points due east. A) The resultant displacement A + B has a magnitude of 3.75 km. What is the magnitude of B and what is the direction of A + B relative to due south? B) Supposed A-B had a magnitude of 3.75km. What then would be the magnitude of B and what is the direction of A-B?

Homework Equations

I made a force triangle of a south arrow A and east arrow B the resultant was drawn from the tail of A to the head of B.
A=2.50km S
B=? E
Resultant = 3.75km

The Attempt at a Solution

I have found B which I got to be 2.80km/s E. using Pythagorean Theorem. A+B is in the direction of South East? This is where I get lost. I have no idea what subtracting vectors does to the direction or basically no idea on subtracting vectors at all. The magnitude of B would be the same though wouldn't it? So basically my question is am I on the right path and to help me find out what I am missing to this question like the direction of A-B. Thank you sooo much, plus any help on vectors would be awsome

 

[LowlyPion]

Welcome to PF.

First of all you don't have force vectors here. You have position vectors.

So that said you really have a position problem. You have a right triangle that you can see immediately.

The runner went south for 2.5. And the hippopotamus is 3.75 from the origin. I reckon you can figure the distance required from Pythagoras right?

And you know the angle to the SE the runner is at because you have the adjacent side and the hippopotamus.

Part B) is just using Pythagoras only this time they give you the 2 sides and ask for the hippo.

 

[KineticNRG]

Your answer to the magnitude (In this case distance) for 'B' is correct, but to state that the direction of A+B is south-east is not accurate, though you are close. To accurately state the direction of A+B you need to know the angle between the vector A and the resultant A+B. As A is the adjacent side to the angle between A and A+B you need to use cosine. Ie: The cosine of angle A A+B = Adjacent(A)/Hypotenuse(A+B). Find the angle by using the inverse cos of A/A+B on your scientific calculator. This angle would need to be 45 for your assumption of south east direction to be correct. You should state the direction as South,X degrees East ( X is your angle that the resultant is away from south, in an easterly direction). Only state South east or north west etc. if the direction is exactly 45 degrees.
As for vector subtraction, you simply add the negative of the vector you are trying to subtract. Eg: Vector A - Vector B is the same as Vector A + (-Vector B). If Vector B was 5km east, then the negative of this vector is 5km West. Simple! I hope this helps you understand vectors a little better.

 

[LowlyPion]

Welcome to PF.

It was not my suggestion that the direction was SE, merely that the angle to that direction, as in general direction, could be easily found through the use of a trig function.

If that was confusing to you, then thanks for clarifying.