# 'Simple' vector problem

1. Nov 11, 2011

### Kaldanis

1. The problem statement, all variables and given/known data
We got this problem in our Physics lecture but maybe it should be in the math section. Anyway, the problem is:

If $\vec{A}+\vec{B} = 6\hat{i} + \hat{j}$, and if $\vec{A}-\vec{B} = -4\hat{i} + 7\hat{j}$, what is the magnitude of $\vec{A}$?

A) 3.0
B) 4.1
C) 5.4
D) 5.8
E) 8.2

3. The attempt at a solution

I drew them out, but other than filling in the angles I'm not quite sure what to do next! I'd appreciate any hints on which direction to go

2. Nov 11, 2011

### BruceW

I guess you could do it geometrically. But there is a faster way. Think of your two equations, and how you could rearrange them to get $\vec{A}$

3. Nov 11, 2011

### Kaldanis

Ohh, I didn't think of solving them as equations. The answer is 2i + 8j which = 8.2? :)

4. Nov 11, 2011

### BruceW

Not quite. When you add both equations together, you get: 2 $\vec{A}$ = 2i + 8j So you need to divide by 2 to get $\vec{A}$

5. Nov 11, 2011

### Kaldanis

I need to stop making stupid mistakes like that! I see the answer is i + 4j = 4.1 now, thank you

6. Nov 11, 2011

### BruceW

yeah, no worries!

7. Nov 11, 2011

### Staff: Mentor

To check your result graphically, draw a line segment between the tips of the two vectors you've drawn (A+B and A-B). Bisect that line segment and call the midpoint point C. Draw a vector from the origin to point C. That'll be vector A. The line segment from C to the tip of the A+B vector will be vector B. The negative of B is the line segment from C to the tip of the A-B vector.