Problem 1E: CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The magnitude of vector u is... Problem 2E: CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The direction angle of vector... Problem 3E:
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence.
3. The horizontal... Problem 4E: CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence.
4. The vertical component,... Problem 5E Problem 6E: CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The vector u= 4,2 is written... Problem 7E Problem 8E: CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. If the dot product of two... Problem 9E Problem 10E Problem 11E Problem 12E: Find the magnitude and direction angle for each vector. See Example 1.
12.
Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E: Write each vector in the form (a, b). Round to four decimal places as applicable. See Example 3.
19.... Problem 20E: Write each vector in the form (a, b). Round to four decimal places as applicable. See Example 3. Problem 21E: Write each vector in the form (a, b). Round to four decimal places as applicable. See Example 3.
21.... Problem 22E: Write each vector in the form (a, b). Round to four decimal places as applicable. See Example 3. Problem 23E: Write each vector in the form (a, b). Round to four decimal places as applicable. See Example 3. Problem 24E: Write each vector in the form (a, b). Round to four decimal places as applicable. See Example 3. Problem 25E: Use the figure to find each vector: (a) u + v (b) u - v (c) u. Use vector notation as in Example 4. Problem 26E:
Use the figure to find each vector: (a) u + v (b) u - v (c) — u. Use vector notation as in Example... Problem 27E: Use the figure to find each vector: (a) u + v (b) u - v (c) — u. Use vector notation as in Example... Problem 28E:
Use the figure to find each vector: (a) u + v (b) u - v (c) — u. Use vector notation as in Example... Problem 29E: Use the figure to find each vector: (a) u + v (b) u - v (c) u. Use vector notation as in Example 4. Problem 30E: Use the figure to find each vector: (a) u + v (b) u - v (c) u. Use vector notation as in Example 4. Problem 31E: Given vectors u and v, find: (a) 2u (b) 2u + 3v (c) v — 3u. See Example 4.
31. u = 2i, v = i + j
Problem 32E: Given vectors u and v, find: (a) 2u (b) 2u + 3v (c) v — 3u. See Example 4.
32. u= -i +2j, v = i - j
Problem 33E: Given vectors u and v, find: (a) 2u (b) 2u + 3v (c) v — 3u. See Example 4.
33. u = (-1, 2), v = (3,... Problem 34E: Given vectors u and v, find: (a) 2u (b) 2u + 3v (c) v - 3u. See Example 4.
34.
Problem 35E: Given u= 2,5 and v= 4,3 , find each of the following. See Example 4. u v Problem 36E: Given u= 2,5 and v= 4,3 , find each of the following. See Example 4. v u Problem 37E: Given and , find each of the following. See Example 4.
37. –4u
Problem 38E:
Given and , find each of the following. See Example 4.
38. –5v
Problem 39E: Given and , find each of the following. See Example 4.
39. 3u – 6v
Problem 40E: Given u= 2,5 and v= 4,3 , find each of the following. See Example 4. 2u +4v Problem 41E:
Given and , find each of the following. See Example 4.
41. u + v – 3u
Problem 42E:
Given and , find each of the following. See Example 4.
42. 2u + v –6v
Problem 43E:
Write each vector in the form ai + bj.
43.
Problem 44E: Write each vector in the form ai + bj. 6,3 Problem 45E: Write each vector in the form ai + bj.
45.
Problem 46E: Write each vector in the form ai + bj. 0,4 Problem 47E: Find the dot product for each pair of vectors. See Example 5. 6,1 , 2,5 Problem 48E: Find the dot product for each pair of vectors. See Example 5. 3,8 , 7,5 Problem 49E Problem 50E: Find the angle between each pair of vectors. See Example 5. 7,2 , 4,14 Problem 51E Problem 52E: Find the dot product for each pair of vectors. See Example 5. 2i + 4j, -j Problem 53E: Find the angle between each pair of vectors. See Example 6. 2,1 , 3,1 Problem 54E: Find the angle between each pair of vectors. See Example 6.
54.
Problem 55E Problem 56E:
Find the angle between each pair of vectors. See Example 6.
56.
Problem 57E Problem 58E Problem 59E: Let u= 2,1 ,v= 3,4 , and w= 5,12 . Evaluate each expression. (3u) v Problem 60E:
Let and . Evaluate each expression.
60. u · (3v)
Problem 61E: Let u= 2,1 ,v= 3,4 , and w= 5,12 . Evaluate each expression. u v u w Problem 62E: Let u= 2,1 ,v= 3,4 , and w= 5,12 . Evaluate each expression. u (v w) Problem 63E: Determine whether each pair of vectors is orthogonal. See Example 6(b). 1,2 , 6,3 Problem 64E: Determine whether each pair of vectors is orthogonal. See Example 6(b). 1,1 , 1,1 Problem 65E: Determine whether each pair of vectors is orthogonal. See Example 6(b). 1,0 , 2,0 Problem 66E:
Determine whether each pair of vectors is orthogonal. See Example 6(b).
66.
Problem 67E: Determine whether each pair of vectors is orthogonal. See Example 6(b). 5i 2j, -5i + 2 5j Problem 68E: Determine whether each pair of vectors is orthogonal. See Example 6(b). -4i + 3j, 8i 6j Problem 69E: (Modeling) Measuring Rainfall Suppose that vector R models the amount of rainfall in inches and the... Problem 70E: Concept Check In Exercise 69, for the rain gauge to collect the maximum amount of water, what should... Problem 71E: Consider the two vectors u and v shown. Assume all values are exact. Work Exercises 71-76 in order.... Problem 72E: Consider the two vectors u and v shown. Assume all values are exact. Work Exercises 71-76 in... Problem 73E: Consider the two vectors u and v shown. Assume all values are exact. Work Exercises 71-76 in order.... Problem 74E Problem 75E Problem 76E: Consider the two vectors u and v shown. Assume all values are exact. Work Exercises 71-76 in order.... Problem 1SE Problem 2SE Problem 3SE: Distance between Two Lighthouses Two lighthouses are located on a north-south line. From lighthouse... Problem 4SE Problem 5SE Problem 6SE Problem 7SE: Wind and Vectors A wind can be described by v = 6i + 8j, where vector j points north and represents... Problem 8SE: 8. Ground Speed and Bearing A plane with an airspeed of 355 mph is on a bearing of 62°. A wind is... Problem 9SE Problem 10SE: Property Survey A triangular piece of property has the dimensions shown. It turns out that the... format_list_bulleted