Homework Help: Few Vector Addition questions, Not sure if correct

1. Sep 9, 2011

Elysian

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

1) Two men are near a hole, One man walks 12m east and then 12m North from a hole, the other walks 15m west and then 11m north, Find the dot product of their net displacements from the tree
_______

2) Vector A = -i +2j - 5k, Vector B = 3i +2j -2k
Find the magnitude and direction of the vector difference A -B

2. Relevant equations

|A||B|cos(t) = A(x)B(x) + A(y)B(y) = |A||B|

3. The attempt at a solution

1 )I didn't calculate the resultant as I think you don't need it, I used the components given

A = 12i + 12j
B = -15i +11j

|A||B| = (12*-15) + (12*11) = -48.

_____________________

2) A - B = -4i -3k

|A-B| = $\sqrt{-4^2 + 0^2 + -3^2}$ = 5.0

arctan($\frac{0}{-4}$ = 0

So the magnitude is 5.0 and the angle is 0 degrees? This seems wrong to me..

If anyone can tell me if I did these right or give me a tip in the right direction, it'd be very much appreciated. Thanks in advance

2. Sep 9, 2011

vela

Staff Emeritus
Don't forget the units.
The formula you used for the angle is for a vector that lies in the xy-plane. You actually have a three-dimensional problem here, so you'll need to think a bit more about how to describe the direction of the vector.

3. Sep 9, 2011

Elysian

Thanks a lot for your reply, For the second one would it actually be arctan z/x? Since there's no y coordinate the vector lies in the xz plane, that would make it arctan z/x?

4. Sep 9, 2011

vela

Staff Emeritus
Yes, that'll work. Just make sure you describe exactly what angle you're calculating.

5. Sep 9, 2011

Elysian

Ok, I've got 36.9 degrees south of west, I think that seems right seeing as this vector is in the 3rd quadrant of the xz axis, from the +x it'd be 216.9 degrees. Have I done anything wrong?

6. Sep 9, 2011

vela

Staff Emeritus
Sounds good.

7. Sep 9, 2011

Elysian

Alright vela, Thanks a ton for your help, I really appreciate it.

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