# 'Simple' vector problem

## Homework Statement

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

## 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 Related Introductory Physics Homework Help News on Phys.org
BruceW
Homework Helper
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 $\vec{A}$

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

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

Not quite. When you add both equations together, you get: 2 $\vec{A}$ = 2i + 8j So you need to divide by 2 to get $\vec{A}$
I need to stop making stupid mistakes like that! I see the answer is i + 4j = 4.1 now, thank you

BruceW
Homework Helper
yeah, no worries!

gneill
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. 