Let $P_1,P_2,P_3$ be $3$ different points in $\mathbb{R}$, then $P_1,P_2,P_3$ form a triangle.
What is the relation between the (one of the) angles of this triangle and $\langle P_2-P_1,P_3-P_1 \rangle$ ?
I am having trouble figuring out which angle of the triangle it is - and even why it is an angle in the triangle...
Note: $\langle ,\rangle$ denotes the standard inner product of $\mathbb{R}^2$.