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If A = (2, 3) and B = (4, 7), find the vector AB.

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Question: If A = (2, 3) and B = (4, 7), find the vector AB.

Options:

  1. (2, 4)
  2. (2, 3)
  3. (2, 1)
  4. (2, 2)

Correct Answer: (2, 4)

Solution: 

Vector AB = B - A = (4 - 2, 7 - 3) = (2, 4).

If A = (2, 3) and B = (4, 7), find the vector AB.

Practice Questions

Q1
If A = (2, 3) and B = (4, 7), find the vector AB.
  1. (2, 4)
  2. (2, 3)
  3. (2, 1)
  4. (2, 2)

Questions & Step-by-Step Solutions

If A = (2, 3) and B = (4, 7), find the vector AB.
  • Step 1: Identify the coordinates of point A, which are (2, 3).
  • Step 2: Identify the coordinates of point B, which are (4, 7).
  • Step 3: To find vector AB, subtract the coordinates of A from the coordinates of B.
  • Step 4: For the x-coordinate, calculate 4 (from B) - 2 (from A) = 2.
  • Step 5: For the y-coordinate, calculate 7 (from B) - 3 (from A) = 4.
  • Step 6: Combine the results from Step 4 and Step 5 to get vector AB = (2, 4).
  • 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 System – Understanding how points are represented in a Cartesian coordinate system.
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