Question 1: Given vectors A = (3, 4) and B = (1, -2), calculate the resultant vector R = A + B.

Answer: (4, 2)

Question 2: Construct vectors C = (5, 2) and D = (-3, 7) on the grid. Find their resultant.

Answer: (2, 9)

Question 3: Two vectors, P = (2, 5) and Q = (3, -1), are added to produce the resultant R. What is R?

Answer: (5, 4)

Question 4: If vector M = (x, 7) and vector N = (4, y), and their resultant is (x+4, y+7), find the resulting vector and explain the process.

Answer: The resultant is (x+4, y+7). To find it, add the corresponding components of M and N.

Question 5: Plot vectors A = (1, 2), B = (4, 3), and their sum on the grid. Confirm the position of the resultant vector.

Answer: (5, 5)

Question 6: Two vectors, X = (x, 4) and Y = (3, y), produce a resultant of (x+3, y+4). If the resultant vector is (7, 9), find x and y.

Answer: x=4, y=5

Question 7: A resultant vector is obtained by adding vectors E = (2, -1) and F = (3, 4). What is the magnitude of the resultant?

Answer: √(5² + 3²) = √34 ≈ 5.83

Question 8: Explain how to determine the resultant of two vectors when they are not aligned along the axes, using the parallelogram rule.

Answer: Place the tail of the second vector at the tip of the first. Complete the parallelogram and draw the diagonal from the common tail point; this diagonal represents the resultant vector.

Question 9: Given vectors G = (x, y) and H = (2x, -3y), find the resultant vector and determine the conditions for its magnitude to be zero.

Answer: Resultant = (3x, -2y). For the magnitude to be zero, x=0 and y=0.

Question 10: Identify and correct the mistake in the following student solution: Adding vectors (2, 3) and (4, 5) incorrectly gives (6, 7).

Answer: The mistake is in the addition. The correct sum is (2+4, 3+5) = (6, 8).

Question 11: Challenge: Two vectors A = (x, y) and B = (-x, 2y) are added to produce a resultant of (0, 3y). Find x and y in terms of y.

Answer: x=0, y=consistent with the resultant; y can be any real number.