Find the coordinates of the AB vector and its length, if A (1; 0; 2), B (-2; 4; 2).

To find the coordinates of a vector, if the coordinates of its beginning and end are specified, it is necessary to subtract the corresponding coordinates of the beginning from the coordinates of the end.
AB = (xb-ha; Yb-Ya; Zb-Za).
Let’s calculate the coordinates of the AB vector:
AB = (- 2-1; 4-0; 2-2) = (- 3; 4; 0).
The length of the AB vector in rectangular Cartesian coordinates is equal to the square root of the sum of the squares of its coordinates.
| AB | = √ (x² + y² + z²).
We calculate the length of the vector AB:
| AB | = √ (x² + y² + z²) = √ ((- 3) ² + 4² + 0²) = √ (9 + 16 + 0) = √25 = 5.
Answer: the coordinates of the vector AB = (- 3; 4; 0), the length of the vector | AB | = 5.