Question 1: Given vectors A = <3, 6> and B = <1, 2>, are these vectors parallel? Show your reasoning.

Answer: Yes, B = 1/3 * A

Question 2: Calculate a scalar multiple k such that the vector <4, -8> is parallel to <2, -4>. Show your working.

Answer: k = 2

Question 3: If vector P = <x, 5> is parallel to vector Q = <10, 15>, find the value of x.

Answer: x = 6

Question 4: Construct two vectors that are parallel to each other but not equal. Use the grid to illustrate your answer.

Answer: Any scalar multiples, e.g., <2, 4> and <1, 2>

Question 5: Determine whether the vectors <7, -3> and <14, -6> are parallel. Show your reasoning.

Answer: Yes, <14, -6> = 2 * <7, -3>

Question 6: A vector A = <x, y> is parallel to vector B = <12, 18>. Find possible values of x and y if x = 3k and y = 4k for some scalar k.

Answer: k = 3, so x = 9, y = 12

Question 7: Plot the graph of y = 2x and draw a vector parallel to <1, 2> that lies on this line.

Answer: Any scalar multiple of <1, 2>, e.g., <3, 6> lies on y=2x

Question 8: Construct a triangle on the grid where two sides are represented by parallel vectors. Describe your construction process.

Answer: Choose a vector, then draw its scalar multiples to form parallel sides.

Question 9: Identify the common mistake in the following reasoning: 'Vectors <5, 10> and <2, 4> are not parallel because their components do not match exactly.' Explain and correct the mistake.

Answer: The mistake is checking components individually rather than scalar multiples. Correct: <2, 4> = 2 * <1, 2>, which is parallel to <5, 10> if scaled appropriately.

Question 10: Find a scalar k such that vector <3, -6> is parallel to <k, 2k>. Show your working.

Answer: k = -3

Question 11: Explain why vectors <8, 4> and <16, 8> are parallel. Use scalar multiplication in your explanation.

Answer: Because <16, 8> = 2 * <8, 4>, they are scalar multiples and thus parallel.