# Math Help - Work of force not working out

1. ## Work of force not working out

I have a question about work done by force:

If a 10N (newton) force acting in the direction of vector (1,1) moves an object from P =(-2,1) to Q=(5,6) calculate the work done. Distance measured in metres.

I did vector PQ
Q-P = (5,6) - (-2,1) = (7,5)
Absolute value PQ = sqrt7^2 + 5^2 = sqrt74

vector (1,1) is a 45 degree angle or 1/sqrt2

next, work = (force)(QP)(1/sqrt2)
10sqrt74(1/sqrt2)

Im getting 5sqrt148 but the correct answer is 60sqrt2

2. The problem is that work is actually equal to the dot product of force with displacement. That is,

$W=\mathbf{F}\cdot\mathbf{d}=\left(\dfrac{10}{\sqrt {2}}\langle 1,1\rangle\right)\cdot\langle 7,5\rangle=\dots$

What do you get when you do that?

3. so i'd do the dot product of (10/sqrt2,10/sqrt2).(7,5)?

I got the answer doing that.

4. That'd work, too (pun intended).