Question 1: Given vectors A = (3, 4) and B = (6, 8), determine if they are parallel. Show your reasoning.

Answer: Yes, B = 2 × A, so they are parallel.

Question 2: Calculate a vector C that is parallel to D = (5, -10) and is a scalar multiple of it with scalar k=3.

Answer: (15, -30)

Question 3: Construct a vector E on the grid that is parallel to vector F = (2, 1) and is 4 times longer.

Answer: (8, 4)

Question 4: Plot the graph of y=2x and draw a vector that is parallel to the vector (1, 2) on the grid.

Answer: Student plots the line and draws a vector with slope 2, such as (1, 2) or (3, 6).

Question 5: Prove that vectors G = (x, y) and H = (2x, 2y) are parallel for all real x, y.

Answer: H = 2 × G for all x, y; thus, G and H are parallel.

Question 6: A ship travels from point A to point B, represented by vector AB = (6, 9). If another ship travels along a vector parallel to AB but with a different magnitude, what could its vector be?

Answer: (12, 18) or (3, 4.5), etc., any scalar multiple.

Question 7: Identify which of the following pairs of vectors are parallel: (2, -4) and (1, -2); (3, 5) and (6, 10); (0, 7) and (7, 0).

Answer: Pairs 1 and 2 are parallel; pair 3 is not.

Question 8: A vector J = (x, y) is parallel to vector K = (4, 8) and passes through the origin. Find the possible values of (x, y).

Answer: (x, y) = (k×4, k×8) for any real k

Question 9: A drone moves along vector L = (7, 14). If it speeds up and moves along a parallel vector, what are two possible vectors it could travel along?

Answer: (14, 28) or (3.5, 7), etc.

Question 10: A student claims vectors (5, 10) and (3, 6) are parallel. Is this correct? Justify your answer.

Answer: No, because (5/3) ≠ (10/6); they are not scalar multiples.

Question 11: Identify and correct the mistake in this statement: 'Vectors (2, 4) and (4, 8) are not parallel because their components are different.'

Answer: Incorrect; vectors are parallel as they are scalar multiples: (2, 4) and (4, 8).