A) Write an expression that can be used to produce vector b from vector a, and explain how you determined that expression. b) Write an expression that can be used to produce vector d from vector c, and explain how you determined that expression.

d) Write an expression that can be used to produce vector r from vectors p and q. Explain how you determined that expression.

Part 3: Solve problems using vectors.
Draw vector diagrams based on the given scenarios, and solve the problems involving vectors.
a) Karina travels 5 miles at a bearing of 30° east of north to get to the supermarket. She then travels 10 miles 15° south of east to go to Anissa’s house. How far away and in what direction is Karina’s house from Anissa’s house? Draw a diagram and show your work to justify your answer. Round the distance to the nearest hundredth and the direction to the nearest degree.

b) An airplane is flying at a constant speed of 500 mph at a bearing of 45° north of west. A 40 mph wind is blowing due south. What are the plane's actual speed and direction? Draw a diagram and show your work to justify your answer. Round the speed to the nearest tenth and the direction to the nearest degree