An object moves along a certain path from point A with position vector $r_1 = 2i + 3j$ to point B with the position vector $r_2 = 3i - 2j$ under the Force $F = i +j$. Find out the work done by the force
What I did
$$W = F* S = (i+j)(r_2-r_1) =(i+j)(3i - 2j - 2i -3j) = -4$$
Answer sheet: 0
It seems like the correct answer is $W=-4$.
For easier computation, note that $W_{total}=W_i+W_j$
The general equation for $Work$: $$W=F*l$$
We calculate $W_1$:
$$W_i = F_i*(r_{2i}-r_{1i})=1*(3-2)=1*1=1$$
Now $W_2$:
$$W_j = F_j*(r_{2j}-r_{1j})=1*(-2-3)=1*(-5)=1$$
So
$W_{total}=W_i+W_j= 1-5=-4$