Find the angle between the vectors AB and AC, if A (- 2; 1), B (2; 5), C (1; – 2).

Place points on the coordinate plane.
Then you need to find the coordinates of the vectors AB and AC
To find the coordinate of the vector, you need to subtract the initial x from the x of course point, and the same with y.
AB = (2 – (- 2); 5-1) = (4; 4)
Similarly AC = (1 – (- 2); -2-1) = (3; -3)
Now let’s find the lengths of these vectors:
| AB | = √ ((x end -x start) ^ 2 + (y end -y start) ^ 2) = √ (4 ^ 2 + 4 ^ 2) = √ (16 + 16)
= √32 = 4√2
| AC | = √ (3 ^ 2 +) – 3) ^ 2) = √ (9 + 9) = √18 = 3√2
cosα = (AB * AC) / (| AB || AC |)
cosα = (4 * 3 +4 * (- 3)) / (4√2 * 3√2) = (12-12) / (4 * 3 * 2) = 0/24 = 0
α = 90 °
Well, the angle between vectors AB and AC = 90 °