The problem asks us to find the vector $AB$ given the points $A = (1, 2, 3)$ and $B = (4, 5, 6)$.

1. Problem Description

The problem asks us to find the vector $AB$ given the points $A = (1, 2, 3)$ and $B = (4, 5, 6)$.

2. Solution Steps

To find the vector $AB$, we subtract the coordinates of point $A$ from the coordinates of point $B$.

$AB = B - A = (4, 5, 6) - (1, 2, 3)$

$AB = (4 - 1, 5 - 2, 6 - 3)$

$AB = (3, 3, 3)$

3. Final Answer

$AB = (3, 3, 3)$