# Simple vector subtraction question

1. Aug 31, 2006

### mikefitz

Greeting everyone, I come to you as a lowly/disgruntled undergrad trying to solve a very simple physics problem. This is the only problem I'm having with my assignment, but I cannot seem to make ANY progress with this one!

I've been given two vectors:

A has magnitude of 5 m and an angle of 55 degrees.
B has a magnitude of 2 m and an angle of 35 degrees.

Here is what I'm supposed to find: Vector C (not shown in the diagram) is the difference of A and B (C = A - B).

What exactly do they mean Vector C? I have no clue what they're talking about - does C begin at the origin?

I don't want the answer given to me, but I would like a sense of direction; thank you so much for your time!

2. Aug 31, 2006

### Saketh

C is a vector that results from subtracting B from A.

By definition, vectors begin at the origin. The endpoint of the vector is its vertex. If I say vector <3, 1>, that means the vector begins at the origin and points to x = 3, y = 1.

You know how to add vectors. You also know what multiplying a vector by -1 does to the vector. So think about subtracting the vector as C = A + (-B).

3. Aug 31, 2006

### mikefitz

Does that mean you are to subtract the magnitude of B from A? - this is the only part of this entire chapter I'm confused on; my book only has a brief write up on the subject and gives no example problems to work on. grr....

4. Aug 31, 2006

### lightgrav

NO! keep track of their directions ...
- B_vector is opposite the B_vector ... points down and to the right.

Add this (Tail-to-tip, like old connect-the-dots) to A,
and C will point from the first tail (at the origin) to the last tip.

5. Sep 1, 2006

### Saketh

When are you adding vectors, you "lift" one of them off of the paper and put its origin point on the arrow point of the other vector. The resulting added vector is the vector that points from the origin to the vertex of the final vector on the chain.

When you are subtracting vectors, you flip one into the opposite direction (due to the negative sign), then add the vectors. The resulting vector is, again, the vector that points from the origin to the final vertex on the chain.

Here is a more descriptive guide to subtracting vectors.

6. Sep 1, 2006

This may or may not be helpful.

The notation I picked up somewhere helps me remember... (i'll just show by an example).

Lets say you have two vectors $\vec A=(3,0)$ and $\vec B =(0,3)$.

Now lets say you want a vector that points from $\vec B$ to $\vec A$

Call this vector $\vec {BA}$

Then just remember to subtract the second part from the first part, such as:
$\vec {BA} = \vec A - \vec B$

Verify this:

$$\vec {BA} = (3-0,0-3)$$

Now notice that if you put the tail of this vector at the head of $\vec B$ the x component moves over 3, and the y component moves down 3, which puts you at the head of vector A.

Side note:
I don't know why the vector symbols is not going accross the entire BA. I don't have time to look up the proper LaTeX for it. But just draw it yourself when doing the problems.

Last edited: Sep 1, 2006
7. Sep 1, 2006

### Staff: Mentor

As FrogPad is suggesting, it is much more practical to add and subtract the vectors' components in rectangular notation. Do you know how to convert the polar notation that you were given (length and angle) to rectangular notation (deltaX, deltaY)?