If A(1, 2, 3) and B(4, 5, 6) are two points, what is the vector AB?

If A(1, 2, 3) and B(4, 5, 6) are two points, what is the vector AB?

Step 1: Identify the coordinates of point A, which are (1, 2, 3).
Step 2: Identify the coordinates of point B, which are (4, 5, 6).
Step 3: To find vector AB, we need to subtract the coordinates of A from the coordinates of B.
Step 4: Calculate the x-component of vector AB: 4 (from B) - 1 (from A) = 3.
Step 5: Calculate the y-component of vector AB: 5 (from B) - 2 (from A) = 3.
Step 6: Calculate the z-component of vector AB: 6 (from B) - 3 (from A) = 3.
Step 7: Combine the components to form vector AB: (3, 3, 3).

Vector Subtraction – The process of finding the vector from point A to point B by subtracting the coordinates of A from the coordinates of B.
Coordinate Geometry – Understanding points in a 3D space and how to manipulate their coordinates.