a) Explain the equation 𝑭 = −𝜵𝑈
dA=F⃗dr⃗=−dU,dA=\vec{F}d\vec{r}=-dU,dA=Fdr=−dU,
F⃗=Fxi⃗+Fyj⃗+Fzk⃗,\vec{F}=F_x\vec{i}+F_y\vec{j}+F_z\vec{k},F=Fxi+Fyj+Fzk,
dr⃗=dxi⃗+dyj⃗+dzk⃗,d\vec{r}=dx\vec{i}+dy\vec{j}+dz\vec{k},dr=dxi+dyj+dzk,
F⃗dr⃗=Fxdx+Fydy+Fzdz=−dU,\vec{F}d\vec{r}=F_xdx+F_ydy+F_zdz=-dU,Fdr=Fxdx+Fydy+Fzdz=−dU,
Fx∂x=−∂U, F_x\partial x=-\partial U,~Fx∂x=−∂U, Fx=−∂U∂x,F_x=-\frac{\partial U}{\partial x},Fx=−∂x∂U,
Fy=∂U∂y,F_y=\frac{\partial U}{\partial y},Fy=∂y∂U, Fz=∂U∂z,F_z=\frac{\partial U}{\partial z},Fz=∂z∂U,
F⃗=−(∂U∂xi⃗+∂U∂yj⃗+∂U∂zk⃗),\vec{F}=-(\frac{\partial U}{\partial x}\vec{i}+\frac{\partial U}{\partial y}\vec{j}+\frac{\partial U}{\partial z}\vec{k}),F=−(∂x∂Ui+∂y∂Uj+∂z∂Uk),
F⃗=−gradU,\vec{F}=-\text{grad}U,F=−gradU,
F⃗=−∇U.\vec{F}=-\nabla U.F=−∇U.
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