Solving Vector Problems: Magnitude of A | Physics & Math Homework

[Kaldanis]

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

 

[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}

 

[Kaldanis]

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]

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}

 

[Kaldanis]

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]

yeah, no worries!

 

[gneill]

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.