Question 1: Calculate the displacement vector from point A (3, 2) to point B (7, 5).

Answer: [4, 3]

Question 2: A student subtracts vectors A = [5, 2] and B = [3, 4], claiming the displacement is [2, -2]. Is this correct? Explain your answer.

Answer: No, the correct displacement vector is [2, -2], which is A - B, so the calculation is correct. The common mistake is mixing up the order of subtraction.

Question 3: Construct a vector diagram showing the displacement from (1, 4) to (6, 9).

Answer: Draw arrows from (1,4) to (6,9), indicating the displacement vector [5, 5].

Question 4: A student calculates the displacement from point P (2, 3) to Q (5, 8) as [3, 4]. Identify and correct the mistake in this calculation.

Answer: The correct displacement vector is [3, 5]. The mistake is in subtracting the y-coordinates; 8 - 3 = 5, not 4.

Question 5: Calculate the displacement vector from (−2, 7) to (4, 3).

Answer: [6, -4]

Question 6: A car moves from (0, 0) to (10, 0) then from (10, 0) to (10, 5). What is the total displacement from the start to the end?

Answer: [10, 5]

Question 7: A vector A = [−3, 4] is subtracted from vector B = [2, -1]. What is the displacement B - A?

Answer: [5, -5]

Question 8: A hiker walks from (2, 3) to (5, 7) then from (5, 7) to (8, 4). What is the overall displacement from the starting point to the final point?

Answer: [6, 1]

Question 9: Identify the common misconception students have when subtracting vectors for displacement and explain how to avoid it.

Answer: A common misconception is reversing the subtraction order or confusing position vectors. To avoid this, always subtract the initial point from the final point: displacement = final − initial.

Question 10: Calculate the displacement vector from (−5, 2) to (3, −4). Then, explain a common mistake made when performing this calculation.

Answer: Displacement = [8, -6]. A common mistake is subtracting in the wrong order or mixing the coordinates, leading to incorrect signs.

Question 11: A robot moves along the points (1, 1), (4, 5), and (6, 2). Calculate the total displacement from the starting point to the final position and identify any misconceptions students might have about vector addition in this context.

Answer: [5, 1]