Given points A (2; 3), B (3; 4), C (5; 2), D (7; 1) Find the coordinates and length of vectors AB

Given points A (2; 3), B (3; 4), C (5; 2), D (7; 1) Find the coordinates and length of vectors AB and CD, the angle between vectors AB and CD.

The coordinates of the vector are equal to the difference between the coordinates of the end and start points:
AB = (3-2; 4-3);
AB = (1; 1);
CD = (7-5; 1-2);
CD = (2; -1).
Find the length of the vector by the Pythagorean theorem:
| AB | = √2;
| CD | = √5;
Let’s find the dot product of vectors:
AB * CD = 1 * 2 + 1 * (-1);
AB * CD = 1.
| AB | * | СD | * cos a = √2 * √5 * cos a;
| AB | * | СD | * cos a = √10 * cos a;
cos a = 1 / √10;
a = arccos (1 / √10);
a ~ 71.6 °.
Answer: a ~ 71.6 °.