Prof. Israel N Nwaguru MATH 1316 CHAPTER 3 - REVIEW
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1 Prof. Israel N Nwaguru MATH 1316 CHAPTER 3 - REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given,, and, use the Law of Sines to solve the triangle for the value of Round answer to two decimal places. 2. Given,, and, use the Law of Sines to solve the triangle for the value of Round answer to two decimal places. 3. Given,, and, use the Law of Sines to solve the triangle for the value of Round answer to two decimal places.
2 4. Given,, and, use the Law of Sines to solve the triangle (if possible) for the value of If two solutions exist, find both. Round answer to two decimal places. not possible 5. Given,, and, use the Law of Sines to solve the triangle (if possible) for the value of If two solutions exist, find both. Round answer to two decimal places. and and not possible 6. Determine the area of a triangle having the following measurements. Round your answer to two decimal places sq. units sq. units sq. units sq. units sq. units 7. Given,, and, use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places. 8. Given,, and, use the Law of Cosines to solve the triangle for the value of C. Round answer to two decimal places. 9. Given,, and, use Heron's Area Formula to find the area of triangle. Round answer to two decimal places sq. units sq. units sq. units sq. units sq. units
3 10. Given,, and, use Heron's Area Formula to find the area of. Round answer to two decimal places sq. units sq. units sq. units sq. units sq. units 11. Find the magnitude of vector v. 12. Find the component form of vector v.
4 13. Find the component form of vector v with initial point and terminal point. 14. Find the magnitude of vector v with initial point and terminal point. 15. Given and, determine. 16. Given and, determine. 17. Find a unit vector in the direction of.
5 18. Find a unit vector in the direction of. 19. Find the vector v that has a magnitude of and is in the same direction as u, where. 20. Let w be a vector with initial point and terminal point. Write w as a linear combination of the standard unit vectors i and j.
6 21. If and, find. 22. Find the magnitude and direction angle of. Round direction angle to nearest degre 23. Find the magnitude and direction angle of. 24. Find the component form of v if and the angle it makes with the x-axis is. 25. Find the component form of v if and the angle it makes with the x-axis is.
7 26. Find the component form of v if and the angle it makes with the x-axis is. 27. Find the component form of v if and the angle it makes with the x-axis is final If and, and the vectors make angles of 0 and 60 and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places. 29. Given and, find Given and, find
8 31. Given vectors and determine the quantity indicated below Given vectors determine whether the result of the following expression is a vector or a scalar. vector scalar 33. Given vectors and determine the quantity indicated below. 34. Use the dot product to find the magnitude of u if Use the dot product to find the magnitude of u if Find the angle between the vectors, and Round answer to two decimal places Find the angle between the vectors and Round answer to two decimal places.
9 Find the angle between the vectors u and v. 39. Determine where is the angle between u and v. Round answer to two decimal places Determine whether u are v and orthogonal, parallel, or neither. neither orthogonal parallel 41. Determine whether u are v and orthogonal, parallel, or neither. parallel neither orthogonal 42. Find the projection of u onto v if,.
10
11 Prof. Israel N Nwaguru MATH 1316 CHAPTER 3 - REVIEW Answer Section MULTIPLE CHOICE 1. ANS: E 2. ANS: D 3. ANS: D 4. ANS: D 5. ANS: A 6. ANS: D 7. ANS: E 8. ANS: D 9. ANS: E 10. ANS: B 11. ANS: A 12. ANS: E 13. ANS: C 14. ANS: C 15. ANS: C 16. ANS: D 17. ANS: E 18. ANS: D 19. ANS: C 20. ANS: B 21. ANS: B 22. ANS: E 23. ANS: E 24. ANS: C 25. ANS: B 26. ANS: D 27. ANS: D 28. ANS: C 29. ANS: E 30. ANS: E 31. ANS: C 32. ANS: B 33. ANS: B 34. ANS: B 35. ANS: B 36. ANS: D 37. ANS: A 38. ANS: A 39. ANS: D 40. ANS: C 41. ANS: B
12 42. ANS: B
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