A body is moving under the action of central force $\vec{F} (r) {\hat{e}}_{r}$ such that its position vector is $\vec{r} = r {\hat{e}}_{r}$ . Then, choose the incorrect statement (symbols are having usual meaning and ${\hat{e}}_{r}, {\hat{e}}_{θ}$ denote unit vectors along the radial and tangential direction, respectively) from the following

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$\vec{v} = \frac{d r}{d t} {\hat{e}}_{r} + r \frac{d θ}{d t} {\hat{e}}_{θ}, \vec{a} = [\frac{d^{2} r}{d t^{2}} - r {(\frac{d θ}{d t})}^{2}] {\hat{e}}_{r}, 2 \frac{d r}{d t} \frac{d θ}{d t} + r \frac{d^{2} θ}{d t^{2}} = 0$

$\vec{v} = \frac{d r}{d t} {\hat{e}}_{r} - r \frac{d θ}{d t} {\hat{e}}_{θ}, \vec{a} = [\frac{d^{2} r}{d t^{2}} + r {(\frac{d θ}{d t})}^{2}] {\hat{e}}_{r}, 2 \frac{d r}{d t} \frac{d θ}{d t} + r \frac{d^{2} θ}{d t^{2}} = 0$

$\vec{v} = \frac{d r}{d t} {\hat{e}}_{r} + r \frac{d θ}{d t} {\hat{e}}_{θ}, \vec{a} = [\frac{d^{2} r}{d t^{2}} + r {(\frac{d θ}{d t})}^{2}] {\hat{e}}_{r}, 2 \frac{d r}{d t} \frac{d θ}{d t} - r \frac{d^{2} θ}{d t^{2}} = 0$

$\vec{v} = \frac{d r}{d t} {\hat{e}}_{r} - r \frac{d θ}{d t} {\hat{e}}_{θ}, \vec{a} = [\frac{d^{2} r}{d t^{2}} - r {(\frac{d θ}{d t})}^{2}] {\hat{e}}_{r}, 2 \frac{d r}{d t} \frac{d θ}{d t} + r \frac{d^{2} θ}{d t^{2}} = 0$