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Math 1316 Professor Merrill Name____________________________ Lab 4 1. Given the vectors AB and CD , find the components of each vector. Let u AB and v CD 2. a. A line has direction vector (2,3). What is the slope?_____________ b. A line has direction vector (4.6). What is the slope?_____________ 3. Find the value of a if the vectors 2,5 and 1, a are a. parallel b. perpendicular 4. All of the following represent vectors except: a. a car heading southeast at 80mph c. a storm traveling west at 25kph b. a barge traveling at 30 knots on a heading of 20o west of south d. a person running on a marathon at 7mph 5. Draw any vector u. Draw any vector v. Now draw 2u + 3v. Be precise! 6. Given A(4, 2) and B(0, -1). Give the component form of AB and find AB Let u = (3, 1), v = (-8, 4) and w = (-6, -2). Find 7. a. u + v b. u – v c. 3u + w 8. Given that u = (8, 45o) and v = (6, -45o), find u v d. u + 1 w 2 9. An airplane has a velocity of 500mph in a southwest direction. A 40mph wind is blowing from the west. Find the resultant speed and direction of the plane. Draw a picture. 10. Riley is swimming on a course of 040o for 4 miles. He realizes how far he is from land and turns to a new heading of 100o and swims for 7 miles. How far is he from his starting point? Draw a picture. 11. Find the component form of the vector, convert it to polar form (show work), find the magnitude. Circle answers Find the sum, difference, or product for the complex numbers. Circle your answer. For the difference, subtract the second number from the first. 12. 14. 11 – 2i and 3 – 4i sum: 13. 7 + 7i and 1 – i sum: difference: difference: product: product: 27 – 13i and 12 + 22i sum: 15. 10 + 2i and 10 sum: difference: difference: product: product: 2i Use the complex conjugate to find the quotient of the two complex numbers. Put answers in the form a + bi 16. 3 3i 6 6i 17. 2 7i 1 i 18. Change the polar coordinates (5.1, 6o) to rectangular coordinates. Set your calculator into radians & polar mode. Type in the following equations. Sketch the graph & answer the questions. Use in [0, 2]. r=a 19. r = a 23. r=3 20. 21. What shape is graphed? 22. What is the radius? r=5 (In window: [0, 4], adjust x & y appropriately to see entire graph) r = .5 24. r = 2 25. What shape to you see? 26. What does the value of a do to the graph? r = a sin b 27. r = 2sin 28. r = 3sin2 29. r = 5cos4 30. r = 3cos3 31. What number determines the number of petals? Explain. 32. Which number determines the length of each petal? r = a + b sin 33. r = 5 + 4cos 34. r = 1 + 3cos 35. The legs of an isosceles triangle are each 21 cm long and the angle between them has a measure of 52. What is the length of the 3rd side? 36. Find the area of triangle XYZ if x = 16, y = 25, and <Z = 52. 37. Find the angle between vectors U and V if U = (2,3) and V = (-3,2)