Answer
$\vec u\cdot\vec v$
Work Step by Step
Step 1. We assume $\vec u=\langle u_x, u_y \rangle$ and $\vec v=\langle v_x, v_y \rangle$
Step 2. Use the projection formula $proj_v\vec u=(\frac{u_xv_x+u_yv_y}{v_x^2+v_y^2})\langle v_x, v_y \rangle$
Step 3. Calculate the dot product $\vec v\cdot (proj_v\vec u)
=(\frac{u_xv_x+u_yv_y}{v_x^2+v_y^2})(v_x^2+v_y^2)
=u_xv_x+u_yv_y=\vec u\cdot\vec v$
