If A(2, 3, 4) and B(1, 0, -1) are two points in space, find the vector AB.
Practice Questions
Q1
If A(2, 3, 4) and B(1, 0, -1) are two points in space, find the vector AB.
(1, 3, 5)
(1, -3, -5)
(1, 3, -5)
(1, -3, 5)
Questions & Step-by-Step Solutions
If A(2, 3, 4) and B(1, 0, -1) are two points in space, find the vector AB.
Correct Answer: (-1, -3, -5)
Step 1: Identify the coordinates of point A, which are (2, 3, 4).
Step 2: Identify the coordinates of point B, which are (1, 0, -1).
Step 3: To find the vector AB, use the formula AB = B - A.
Step 4: Calculate the x-component of AB: 1 (from B) - 2 (from A) = -1.
Step 5: Calculate the y-component of AB: 0 (from B) - 3 (from A) = -3.
Step 6: Calculate the z-component of AB: -1 (from B) - 4 (from A) = -5.
Step 7: Combine the components to get the vector AB: (-1, -3, -5).
Step 8: If needed, express the vector in the opposite direction: (1, 3, 5).
Vector Subtraction – The question tests the understanding of how to find the vector from point A to point B by subtracting the coordinates of A from B.
Coordinate System – It assesses the ability to work with points in a three-dimensional coordinate system.
