Given points A (0 and -3) B (-1 and 0) C (5 and 2) Find the coordinates and length of the vector AB.

Let’s find the coordinates of the vector AB, subtracting the coordinates of the beginning of the vector from the coordinates of the end of the vector, as a result we get:
AB = {-1 – 0; 0 + 3} = {-1; 3}
Let’s find the length of this vector as the square root of the sum of the squares of the coordinates:
| AB | = ((-1) ^ 2 + 3 ^ 2) ^ (1/2) = (1 + 9) ^ (1/2) = √10
Answer: AB = {-1; 3}
| AB | = √10