$\overrightarrow{\mathrm{v}}=\frac{\mathrm{d} \overrightarrow{\mathrm{r}}}{\mathrm{dt}}=(\cos t \hat{i}-\sin t \hat{j})$

$\overrightarrow{\mathrm{a}}=\frac{\mathrm{d} \overrightarrow{\mathrm{v}}}{\mathrm{dt}}=(-\sin t \hat{\mathrm{i}}-\cos t \hat{\mathrm{j}})$

According to question

$\overrightarrow{r} \cdot \overrightarrow{a}=0$

$\Rightarrow-\sin ^{2} t-\cos ^{2} t=0$

$\Rightarrow 1=0$ which is not possible