Vector Subtraction: S-T Magnitude Explained

[savageqm]

This is my first time leaning physics and the vectors are really hard to understand so far(doesn't help that the teacher has not taught it in depth)

am reading the book and they have a sample problem that states:
S=3 m and T=4 m

The question is what is the magnitude of the difference vectors S - T.

The books shows three answers which is; 7m, 5m and 1m

please explain me how they came up with these answers.

7m I think I understand because they added 3 + (-4), but the rest am lost.

 

[PhanthomJay]

If S and T are vectors, they must have a direction. Are they given?

 

[savageqm]

well that books just shows them with the arrows on top pointing the same way but T is negative.

 

[PhanthomJay]

If the arrows are pointing in the same direction, then to add them, you just get 7m pointing in the same direction as the original vectors. But what if you subtract T from S...then what do you get

Edit: are these 3 different questions or one multiple choice question. A picture might help or a better description. When you subtract vectors, S and T, then S - T = S + (-T). The minus in front of the T implies that you change the direction of T so its pointing in the opposite direction.

 

[savageqm]

maybe this will help.
http://cid-3c099006138591f8.photos.live.com/self.aspx/Public/DSCN7108.JPG"

 

[PhanthomJay]

OK, you have 2 vectors, S and T, which you can point in any direction you choose, and now you want to calculate S - T, for different directions of those vectors. The magnitude of S is 3, and the magnitude of T is 4. You seem to have found one solution, when the S vector is 3 units to the right, and the T vector is 4 units to the left, then their vector difference (S - T) is 7 units to the right, and the magnitude of that result is 7. But what if the S vector is 3 units to the right, and the T vector is 4 units to the right. What's the magnitude of the vector difference then? And what if S and T are at right angles (perpendicular) to each other? Then you'll have to find the magnitude of the resultant difference by using the Pythagorean Theorem ( are you familiar with that ? Hint..what's the diagonal measure?).

Now play around with graphing the resultant vector for different directions, using rough sketches. The resultant can never be bigger than a certain number, nor less than another certain number.