# Homework Help: Distance between two vectors

1. Sep 6, 2011

1. The problem statement, all variables and given/known data

You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don't pitch your tents close together. Joe's tent is 24.0 m from yours, in the direction 23.0 degrees north of east. Karl's tent is 43.5 m from yours, in the direction 41.0 degrees south of east.

What is the distance between Karl's tent and Joe's tent?

2. Relevant equations

Karl's tent dk = 32.83{i) -28.54{j}
Joe's tent dj = 22.09{i}+ 9.38{j}

3. The attempt at a solution

Karl's tent dk = 32.83{i) -28.54{j}
Joe's tent dj = 22.09{i}+ 9.38{j}

dkj=dkjx{i}+dkjy{j}

9.38 + dkjy=-28.54
22.09{i}+dkjx=32.83

22.09-32.83= -10.74
9.38+28.54 = 37.92

(10.74)2+(37.92)2 and then square root = 39.41m.

Is that right. Thanks!

Last edited: Sep 6, 2011
2. Sep 6, 2011

### lewando

Final answer looks too big. Assuming your location is at the origin, dj looks fine, but shouldn't dk have a negative j component?

3. Sep 6, 2011

Ok, I changed it to 39.41 meters.

Last edited: Sep 6, 2011
4. Sep 6, 2011

### lewando

Much better !

5. Sep 6, 2011