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.