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**1. Homework Statement**

We got this problem in our Physics lecture but maybe it should be in the math section. Anyway, the problem is:

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

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