# Unit vectors

1. Feb 12, 2008

### chocolatelover

1. The problem statement, all variables and given/known data
Vector A=3i-1j and B=-i-4j
Find vector A-B and|vector A-B|

2. Relevant equations

3. The attempt at a solution

Vector A-B=4i-3j

Is the |vector A-B|the magnitude or just the absolute value of the answer?

Thank you very much

2. Feb 12, 2008

### ranger

|A| is the magnitude of a vector A. To avoid confusion, one can use ||A|| to denote magnitude.

3. Feb 12, 2008

### chocolatelover

Thank you very much

Is the other part correct? The magnitude is the same thing as the angle of the vector, right? Is there a formula for calculating the magnitude?

Thank you

Last edited: Feb 12, 2008
4. Feb 12, 2008

### ranger

The magnitude of a vector whose components are <a1, a2> (2 dimensional vector) is:

$$\sqrt{a_1^2 + a_2^2}$$
Please do not confuse magnitude and direction. Although they are both characteristics of a vector, they are different things.

Recheck A-B, the j component has its sign messed up.

5. Feb 12, 2008

### chocolatelover

Thank you very much

4i+5j does that look correct?

6. Feb 12, 2008

### ranger

Recheck.
Let A = <a1, a2> and B = <b1, b2>

A-B = <a1-b1, a2-b2>

7. Feb 12, 2008

### chocolatelover

If vector A=3i-1j
and B=-1i-4j

in order to find A-B, don't you just do 3i--1i=4i and -1i--4j=3j

Wouldn't it be 4i+3j?

and is the magnitude of A-B 6.40?

Thank you

Last edited: Feb 12, 2008
8. Feb 12, 2008

### ranger

Yup 4i+3j is correct. You made the mistake of writing 4i-3j in your initial post.

9. Feb 12, 2008

### chocolatelover

Thank you very much

Regards

10. Feb 12, 2008

### ranger

But your magnitude doesnt look too good. Recheck that.

11. Feb 12, 2008

Thank you