If A(1, 2, 3) and B(4, 5, 6) are two points in space, what is the vector AB?
Correct Answer: (3, 3, 3)
- 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 point A from the coordinates of point 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 Representation – Understanding how to represent vectors in space using coordinates.
- Vector Subtraction – Applying the concept of vector subtraction to find the vector from point A to point B.
