# Vector decomposition

1. Aug 25, 2016

### Turbodog66

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

The force on an object is F = -11j. For the vector v =-i-5j, find:

1. The component of F parallel to v
2. The component of F perpendicular to v
3. The work, W, done by force F through displacement v

2. Relevant equations

ProjvF = v dot F/ |v|2
OrthvF = F - ProjvF
W = D dot F

3. The attempt at a solution

F = < 0, -11> v = < -1, -5>

1.
ProjvF = -1(0) + -5(-11) / 12 + -52 = 55/26<-1, -5>
ProjvF = <-2.115, -10.576>

2.
OrthvF = < 0, -11> - <-2.115, -10.576> = 0 + 2.115 , -11 +10.576 = <2.115, -0.424>
OrthvF = <2.115, -0.424>

3.
W = <2.115, -0.424> dot < 0, -11> = 2.115(0) + -0.424(-11) = 4.664
W = 4.664

I am told that step 1 is correct, and the first value in step 2 is correct. I cannot figure out what I am missing on part 2, which is ultimately messing up step 3. Any help would be appreciated.

2. Aug 25, 2016

### BvU

In 3 you don't do $\vec v\cdot\vec F$ but you use the one that's perpendicular.
In 2 I don't see what's wrong.

3. Aug 25, 2016

### Turbodog66

Thanks, I see what I did wrong on part 3. Part 2 after redoing it again was expecting -0.42307, I rounded too soon it seems