Problem 1E: Name all the equal vectors in the parallelogram shown. Problem 2E: Write each combination of vectors as a single vector. (a) AB+BC (b) CD+DB (c) DBAB (d) DC+CA+AB Problem 3E Problem 4E: Copy the vectors in the figure and use them to draw the following vectors. (a) a + b (b) a b (c)... Problem 5E: 58 Find a vector a with representation given by the directed line segment AB. Draw AB and the... Problem 6E: 58 Find a vector a with representation given by the directed line segment AB. Draw AB and the... Problem 7E: Find a vector a with representation given by the directed line segment AB. Draw AB and the... Problem 8E: 58 Find a vector a with representation given by the directed line segment AB. Draw AB and the... Problem 9E: Find the sum of the given vectors and illustrate geometrically. 15. 1, 4, 6, 2 Problem 10E: Find the sum of the given vectors and illustrate geometrically. 16. 3, 1, 1, 5 Problem 11E: Find the sum of the given vectors and illustrate geometrically. 17. 3, 0, 1, 0, 8, 0 Problem 12E: Find the sum of the given vectors and illustrate geometrically. Problem 13E: Find a + b, 2a + 3b, |a|, and |a b|. 13. a = 5, 12, b = 3, 6 Problem 14E: Find a + b, 2a + 3b, |a|, and |a b|. 14. a = 4i + j, b = i 2j Problem 15E: Find a + b, 2a + 3b, |a|, and |a b|. 15. a = i + 2j 3k, b = 2i j + 5k Problem 16E: Find a + b, 2a + 3b, |a|, and |a b|. 16. a = 2i 4j + 4k, b = 2j k Problem 17E: Find a unit vector that has the same direction as the given vector. 25. 8i j + 4k Problem 18E: Find a vector that has the same direction as 2,4,2 but has length 6. Problem 19E Problem 20E Problem 21E: If v lies in the first quadrant and makes an angle /3 with the positive x-axis and | v | = 4, find v... Problem 22E Problem 23E Problem 24E: Find the magnitude of the resultant force and the angle it makes with the positive x-axis. 33. Problem 25E: Find the magnitude of the resultant force and the angle it makes with the positive x-axis. 33. Problem 26E Problem 27E: A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 22... Problem 28E: Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town... Problem 29E: A clothesline is tied between two poles, 8 m apart. The line is quite taut and has negligible sag.... Problem 30E: The tension T at each end of a chain has magnitude 25 N (see the figure). What is the weight of the... Problem 31E: A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream from... Problem 32E: Three forces act on an object. Two of the forces are at an angle of 100 to each other and have... Problem 33E: Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (2,... Problem 34E Problem 35E: (a) Draw the vectors a = 3, 2, b = 2, 1, and c = 7, 1. (b) Show, by means of a sketch, that there... Problem 36E: Suppose that a and b are nonzero vectors that are not parallel and c is any vector in the plane... Problem 37E: If r = x, y, z and r0 = x0, y0, z0, describe the set of all points (x, y, z) such that | r r0 | =... Problem 38E: If r = x, y, r1 = x1, y1, and r2 = x2, y2, describe the set of all points (x, y) such that | r r1 |... Problem 39E: Figure 16 gives a geometric demonstration of Property 2 of vectors. Use components to give an... Problem 40E: Prove Property 5 of vectors algebraically for the case n =3. Then use similar triangles to give a... Problem 41E: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to... format_list_bulleted