Find the point on the line \(y=2x+3\) that is closest to the origin.

To prove : The similarity of \(\displaystyle\triangle{N}{R}{T}\) with respect to \(\displaystyle\triangle{N}{S}{P}\). Given information: Here, we have given that \(\displaystyle\overline{{{S}{P}}}\) is altitude to \(\displaystyle\overline{{{N}{R}}}\ {\quad\text{and}\quad}\ \overline{{{R}{T}}}\) is altitude to \(\displaystyle\overline{{{N}{S}}}\).

If A, B, and C are the vertices of a triangle, find \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}\)