Question 1: Displacement is the change in position of an object, represented by the difference between the position vectors of the starting and ending points. Mathematically, if points A and B have position vectors \( \vec{A} \) and \( \vec{B} \), then the displacement from A to B is \( \vec{B} - \vec{A} \).

Answer:

Question 1: Calculate the displacement vector from point P(3, 4) to point Q(7, 9).

Answer: [4, 5]

Question 2: Point A has position vector (2, -1). Point B has position vector (5, 2). Find the displacement vector from A to B.

Answer: [3, 3]

Question 3: Construct a displacement vector from point C(0, 0) to point D(6, 8) on the grid.

Answer: [6, 8]

Question 4: Point E is at (−3, 4). Point F is at (2, −1). Calculate the displacement vector from E to F.

Answer: [5, -5]

Question 5: Plot the vector from (1, 2) to (4, 5) on the provided grid.

Answer:

Question 6: A person walks from point G(2, 3) to point H(5, 7). What is the displacement vector?

Answer: [3, 4]

Question 7: A robot moves from position (−2, 5) to (3, 1). Determine its displacement vector.

Answer: [5, -4]

Question 8: Construct a triangle with vertices at (0, 0), (4, 0), and (4, 3). Calculate the displacement from the origin to the top vertex.

Answer: [4, 3]

Question 9: Explain why subtracting vectors \( \vec{A} = [2, 3] \) and \( \vec{B} = [5, 1] \) gives the displacement from A to B.

Answer: Because displacement from A to B is \( \vec{B} - \vec{A} = [5-2, 1-3] = [3, -2] \), representing how far and in which direction B is from A.

Question 10: A cyclist travels from point I(1, 2) to point J(4, 6). If they then change direction to point K(2, 8), what is the overall displacement from I to K?

Answer: Displacement from I to J is [3, 4], from J to K is [−2, 2], total displacement is [1, 6].

Question 11: Identify and correct the mistake: A student calculates displacement as \( \vec{A} + \vec{B} \) instead of \( \vec{B} - \vec{A} \).

Answer: The mistake is adding vectors instead of subtracting. Displacement from A to B is \( \vec{B} - \vec{A} \), not \( \vec{A} + \vec{B} \).