Why is there a dr in the second term of the gravitational force equation?

[REVIANNA]

Homework Statement

Homework Equations

I know that
##F_g=(G*m_e*m)/r^2)##
##dr⃗ =drr_1+rdθθ_1.##

##F⃗ g⋅dr⃗ =−(Gm_em/r^2)*r_1⋅(drr_1+rdθθ_1)##

##F⃗ g⋅dr⃗ =−(Gm_em/r^2)(drr_1⋅r_1+r*dr*dθ*θ_1⋅r_1)##

The Attempt at a Solution

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I don't understand why there is a dr in the 2nd term in the second bracket.
I have used r_1 and ##theta_1## for unit vectors.
I know how to proceed from this step (##r_1.r_1=1## whereas ##theta_1.r_1=0(perpendicular)##

 

[andrewkirk]

I don't understand why there is a dr in the 2nd term in the second bracket.

There should not be a ##dr## there. It looks like a mistake.
In any case it doesn't matter, as the term is zero because the dot product is.

 

[REVIANNA]

In any case it doesn't matter, as the term is zero because the dot product is.

yes as unit vector θ and unit vector r are perpendicular .
thanks.