Question 1: The resultant vector of two vectors is found by adding their corresponding components. If vectors are represented as columns, the resultant is the sum of these columns. The formula for the resultant R of vectors A and B is R = A + B.

Answer: R = A + B

Question 1: Given vector A = [3, 4] and vector B = [1, 2], find the resultant vector R.

Answer: [4, 6]

Question 2: Calculate the sum of vectors A = [−2, 5] and B = [7, −3].

Answer: [5, 2]

Question 3: Add vectors A = [0, 6] and B = [4, −2]. What is the resultant?

Answer: [4, 4]

Question 1: A boat moves 5 km east and then 3 km north. Represent these movements as vectors and find the resultant displacement vector.

Answer: [~5.83, ~3.0]

Question 2: Two forces are applied to an object: Force A = [6, 2] and Force B = [−3, 4]. What is the combined force acting on the object?

Answer: [3, 6]

Question 3: A cyclist travels 10 km south and then 8 km west. Find the resultant vector representing the cyclist's net displacement.

Answer: [−8, −10]

Question 4: If vector P = [2, −3] and vector Q = [4, 5], what is P + Q?

Answer: [6, 2]

Question 5: Add vectors [−1, 7] and [3, −4]. What is the resultant?

Answer: [2, 3]

Question 1: A drone flies 12 km northeast and then 5 km southeast. Represent these movements as vectors and find the resultant vector.

Answer: [~13.0, 3.0]

Question 2: A hiker walks 8 km west and then 6 km south. What is the resultant displacement vector?

Answer: [-8, -6]

Question 1: Combine vectors [3, −2] and [−1, 4] and verify your answer by calculating the magnitude of the resultant.

Answer: {"vector":"[2, 2]","magnitude":"≈2.83"}

Question 2: A car moves 15 km east and then 20 km north. Find the resultant displacement and its approximate magnitude.

Answer: [~23.54, ~15]

Question 1: Student's incorrect addition: [2, 5] + [3, −2] = [5, 3]. Find the mistake and give the correct resultant.

Answer: Incorrect addition of y-components. Correct resultant: [5, 3]