Problem 1E: Interpret the following statement: Points have a location, but no size or direction; nonzero vectors... Problem 2E: What is a position vector? Problem 3E Problem 4E Problem 5E: Given a position vector v, why are there infinitely many vectors equal to v? Problem 6E Problem 7E Problem 8E Problem 9E: If u = u1, u2 and v = v1, v2, how do you find u + v? Problem 10E Problem 11E Problem 12E: Express the vector v = v1, v2 in terms of the unit vectors i and j. Problem 13E: How do you compute |PQ| from the coordinates of the points P and Q? Problem 14E Problem 15E: How do you find a vector of length 10 in the direction of v = 3, 2? Problem 16E Problem 17E: Vector operations Refer to the figure and carry out the following vector operations. 17. Scalar... Problem 18E: Vector operations Refer to the figure and carry out the following vector operations. 18. Scalar... Problem 19E: Vector operations Refer to the figure and carry out the following vector operations. 19. Scalar... Problem 20E: Vector operations Refer to the figure and carry out the following vector operations. 20. Scalar... Problem 21E Problem 22E: Vector operations Refer to the figure and carry out the following vector operations. 22. Vector... Problem 23E: Components and magnitudes Define the points O(0, 0), P(3, 2), Q(4, 2), and R(6, 1). For each vector,... Problem 24E Problem 25E: Components and equality Define the points P(3, 1), Q(1, 2), R(1, 2), S(3, 5), T(4, 2), and U(6, 4).... Problem 26E: Components and equality Define the points P(3, 1), Q(1, 2), R(1, 2), S(3, 5), T(4, 2), and U(6, 4).... Problem 27E: Components and equality Define the points P(3, 1), Q(1, 2), R(1, 2), S(3, 5), T(4, 2), and U(6, 4).... Problem 28E: Vector operations Let u = 4, 2, v = 4, 6, and w = 0, 8. Express the following vectors in the form a,... Problem 29E: Vector operations Let u = 4, 2, v = 4, 6, and w = 0, 8. Express the following vectors in the form a,... Problem 30E: Vector operations Let u = 4, 2, v = 4, 6, and w = 0, 8. Express the following vectors in the form a,... Problem 31E: Vector operations Let u = 4, 2, v = 4, 6, and w = 0, 8. Express the following vectors in the form a,... Problem 32E: Vector operations Let u = 4, 2, v = 4, 6, and w = 0, 8. Express the following vectors in the form a,... Problem 33E: Vector operations Let u = 4, 2, v = 4, 6, and w = 0, 8. Express the following vectors in the form a,... Problem 34E: Vector operations Let u = 3, 4, v = 1, 1, and w = 1, 0. 34. Find |u + v|. Problem 35E: Vector operations Let u = 3, 4, v = 1, 1, and w = 1, 0. 35. Find |2v|. Problem 36E: Vector operations Let u = 3, 4, v = 1, 1, and w = 1, 0. 36. Find |u + v + w|. Problem 37E: Vector operations Let u = 3, 4, v = 1, 1, and w = 1, 0. 37. Find |2u + 3v 4w|. Problem 38E Problem 39E: Vector operations Let u = 3, 4, v = 1, 1, and w = 1, 0. 39. Find two vectors parallel to v with... Problem 40E Problem 41E: Vector operations Let u = 3, 4, v = 1, 1, and w = 1, 0. 41. Which has the greater magnitude, u v or... Problem 42E Problem 43E Problem 44E Problem 45E: Unit vectors Define the points P(4, 1), Q(3, 4), and R(2, 6). 45. Find two unit vectors parallel to... Problem 46E Problem 47E Problem 48E: A boat in a current The water in a river moves south at 10 mi/hr. A motorboat travels due east at a... Problem 49E: Another boat in a current The water in a river moves south at 5 km/hr. A motorboat travels due east... Problem 50E Problem 51E Problem 52E Problem 53E: Boat in a wind A sailboat floats in a current that flows due east at 1 m/s. Due to a wind, the boats... Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E Problem 59E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 60E Problem 61E: Unit vectors a. Find two unit vectors parallel to v = 6i 8j. b. Find b if v=13,b is a unit vector.... Problem 62E: Equal vectors For the points A(3, 4), B(6, 10), C(a + 2, b + 5), and D(b + 4, a 2), find the values... Problem 63E: Vector equations Use the properties of vectors to solve the following equations for the unknown... Problem 64E: Vector equations Use the properties of vectors to solve the following equations for the unknown... Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E: Solving vector equations Solve the following pairs of equations for the vectors u and v. Assume i =... Problem 72E Problem 73E: Designer vectors Find the following vectors. 73. The vector in the direction of 5, 12 with length 3 Problem 74E: Designer vectors Find the following vectors. 74. The vector in the direction opposite that of 6, 8... Problem 75E: Designer vectors Find the following vectors. 75. The position vector for your final location if you... Problem 76E: Ant on a page An ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on... Problem 77E: Clock vectors Consider the 12 vectors that have their tails at the center of a (circular) clock and... Problem 78E: Three-way tug-of-war Three people located at A, B, and C pull on ropes tied to a ring. Find the... Problem 79E Problem 80E Problem 81E: Additional Exercises 8185. Vector properties Prove the following vector properties using components.... Problem 82E: Additional Exercises 8185. Vector properties Prove the following vector properties using components.... Problem 83E: Vector properties Prove the following vector properties using components. Then make a sketch to... Problem 84E: Vector properties Prove the following vector properties using components. Then make a sketch to... Problem 85E: Vector properties Prove the following vector properties using components. Then make a sketch to... Problem 86E Problem 87E: Magnitude of scalar multiple Prove that |cv| = |c| |v|, where c is a scalar and v is a vector. Problem 88E: Equality of vectors Assume PQ equals RS. Does it follow that PR is equal to QS? Explain your answer. Problem 89E: Linear independence A pair of nonzero vectors in the plane is linearly dependent if one vector is a... Problem 90E: Perpendicular vectors Show that two nonzero vectors u = u1, u2 and v = v1, v2 are perpendicular to... Problem 91E: Parallel and perpendicular vectors Let u = a, 5 and v = 2, 6. a. Find the value of a such that u is... Problem 92E: The Triangle Inequality Suppose u and v are vectors in the plane. a. Use the Triangle Rule for... format_list_bulleted
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning