Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN: 9781337278461
Author: Ron Larson
Publisher: Cengage Learning
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Magnitude
A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector spa…
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Chapter 3.4, Problem 27E

Finding the Magnitude of a Vector In Exercises 23 - 28 , use the dot product to find the magnitude of u

u = 6 j

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Chapter 3.4, Problem 26E
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Chapter 3 Solutions

Trigonometry (MindTap Course List)

Ch. 3.1 - For the triangle shown, A=30, B=45, and a=32...Ch. 3.1 - Find the height of the tree shown in the figure.Ch. 3.1 - Given A=31,a=12 inches, and b=5 inches, find the...Ch. 3.1 - Show that there is no triangle for which a=4 feet,...Ch. 3.1 - Prob. 5ECPCh. 3.1 - Find the area of a triangular lot with two sides...Ch. 3.1 - On a small lake, you swim from point A to point B...Ch. 3.1 - Prob. 1ECh. 3.1 - For triangle ABC, the Law of Sines is...Ch. 3.1 - Prob. 3E
Ch. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Using the Law of Sines In Exercises 5-22, use the...Ch. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Using the Law of Sines In Exercises 23-32, use the...Ch. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Using the Law of Sines In Exercises 23–32, use the...Ch. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Finding the Area of a Triangle In Exercises 37-44,...Ch. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Height A tree grows at an angle of 4 from the...Ch. 3.1 - A boat is traveling due east parallel to the...Ch. 3.1 - Environmental Science The bearing from the Pine...Ch. 3.1 - Bridge Design A bridge is built across a small...Ch. 3.1 - Angle of Elevation A 10 -meter utility pole casts...Ch. 3.1 - Flight Path A plane flies 500 kilometers with ab...Ch. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Distance Air traffic controllers continuously...Ch. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - True or False? In Exercises 55-58, determine...Ch. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.2 - Find the three angles of the triangle whose sides...Ch. 3.2 - Given A=80,b=16 meters, and c=12 meters, find the...Ch. 3.2 - In a softball game, a batter hits a ball to dead...Ch. 3.2 - Prob. 4ECPCh. 3.2 - Prob. 5ECPCh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Solving a Triangle In Exercises 31-36, determine...Ch. 3.2 - Prob. 37ECh. 3.2 - Using Heron’s Area Formula In Exercises 37-44, use...Ch. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Surveying To approximate the length of a marsh, a...Ch. 3.2 - Streetlight design Determine the angle in the...Ch. 3.2 - Baseball A baseball player in center field is...Ch. 3.2 - Baseball On a baseball diamond with 90-foot sides,...Ch. 3.2 - Prob. 49ECh. 3.2 - Navigation On a map, Minneapolis is 165...Ch. 3.2 - Navigation A boat race runs along a triangular...Ch. 3.2 - Air Navigation A plane flies 810 miles from...Ch. 3.2 - Surveying A triangular parcel of land has 115...Ch. 3.2 - Prob. 54ECh. 3.2 - Distance Two ships leave a port at 9.M.. One...Ch. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - True or False? In Exercises 61 and 62, determine...Ch. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - HOW DO YOU SEE IT? To solve the triangle, would...Ch. 3.2 - Prob. 67ECh. 3.3 - Show that u and v in the figure at the right are...Ch. 3.3 - Prob. 2ECPCh. 3.3 - Prob. 3ECPCh. 3.3 - Prob. 4ECPCh. 3.3 - Prob. 5ECPCh. 3.3 - Prob. 6ECPCh. 3.3 - Prob. 7ECPCh. 3.3 - Prob. 8ECPCh. 3.3 - Prob. 9ECPCh. 3.3 - Prob. 10ECPCh. 3.3 - Prob. 11ECPCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Prob. 41ECh. 3.3 - Finding a Unit Vector In Exercises 4146, find a...Ch. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Prob. 44ECh. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Writing a Linear Combination of Unit Vectors In...Ch. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.3 - Prob. 64ECh. 3.3 - Prob. 65ECh. 3.3 - Prob. 66ECh. 3.3 - Prob. 67ECh. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Using the Law of Cosines In Exercises 73 and 74,...Ch. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Prob. 76ECh. 3.3 - Prob. 77ECh. 3.3 - Velocity Pitcher Aroldis Chapman threw a pitch...Ch. 3.3 - Prob. 79ECh. 3.3 - Prob. 80ECh. 3.3 - Prob. 81ECh. 3.3 - Prob. 82ECh. 3.3 - Cable Tension The cranes shown in the figure are...Ch. 3.3 - Prob. 84ECh. 3.3 - Prob. 85ECh. 3.3 - Physics Use the figure to determine the tension...Ch. 3.3 - Prob. 87ECh. 3.3 - Prob. 88ECh. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Air Navigation An airplane travels in the...Ch. 3.3 - Prob. 94ECh. 3.3 - Prob. 95ECh. 3.3 - True or False? In Exercises 9598, determine...Ch. 3.3 - True or False? In Exercises 9598, determine...Ch. 3.3 - Prob. 98ECh. 3.3 - Error Analysis Describe the error in finding the...Ch. 3.3 - Prob. 100ECh. 3.3 - Prob. 101ECh. 3.3 - Technology Write a program for your graphing...Ch. 3.3 - Finding the Difference of Two Vectors In Exercises...Ch. 3.3 - Finding the Difference of Two Vectors In Exercises...Ch. 3.3 - Graphical Reasoning Consider two forces...Ch. 3.3 - Prob. 106ECh. 3.3 - Prob. 107ECh. 3.3 - Prob. 108ECh. 3.4 - Find each dot product. a. 3,42,3 b. 3,51,8 c....Ch. 3.4 - Prob. 2ECPCh. 3.4 - Find the angle between u=2,1 and v=1,3.Ch. 3.4 - Prob. 4ECPCh. 3.4 - Prob. 5ECPCh. 3.4 - Prob. 6ECPCh. 3.4 - Prob. 7ECPCh. 3.4 - Prob. 1ECh. 3.4 - Vocabulary: Fill in the blanks. The dot product of...Ch. 3.4 - Prob. 3ECh. 3.4 - Fill in the blanks. The vectors u and v are if...Ch. 3.4 - Fill in the blanks. The projection of u onto v is...Ch. 3.4 - Fill in the blanks. The work W done by a constant...Ch. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Using the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Decomposing a Vector into Components In Exercises...Ch. 3.4 - Decomposing a Vector into Components In Exercises...Ch. 3.4 - Prob. 59ECh. 3.4 - Prob. 60ECh. 3.4 - Finding the Projection of u onto v In Exercises...Ch. 3.4 - Prob. 62ECh. 3.4 - Prob. 63ECh. 3.4 - Prob. 64ECh. 3.4 - Prob. 65ECh. 3.4 - Prob. 66ECh. 3.4 - Prob. 67ECh. 3.4 - Prob. 68ECh. 3.4 - Prob. 69ECh. 3.4 - Prob. 70ECh. 3.4 - Business The vector u=1225,2445 gives the numbers...Ch. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.4 - Prob. 75ECh. 3.4 - Work Determine the work done by a crane lifting a...Ch. 3.4 - Prob. 77ECh. 3.4 - Prob. 78ECh. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.4 - Prob. 81ECh. 3.4 - Prob. 82ECh. 3.4 - Prob. 83ECh. 3.4 - True or False? In Exercises 83 and 84, determine...Ch. 3.4 - Prob. 85ECh. 3.4 - Prob. 86ECh. 3.4 - Prob. 87ECh. 3.4 - Prob. 88ECh. 3.4 - Prob. 89ECh. 3.4 - Prob. 90ECh. 3.4 - Prob. 91ECh. 3.4 - Prob. 92ECh. 3.4 - Prob. 93ECh. 3 - Prob. 1RECh. 3 - Using the Law of Sines In Exercises 112, use the...Ch. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - River Width A surveyor finds that a pier on the...Ch. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Geometry The lengths of the sides of a...Ch. 3 - Prob. 38RECh. 3 - Surveying To approximate the length of a marsh, a...Ch. 3 - Air Navigation Two planes leave an airport at...Ch. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - Prob. 57RECh. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Prob. 75RECh. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Prob. 81RECh. 3 - Prob. 82RECh. 3 - Prob. 83RECh. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Prob. 93RECh. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 97RECh. 3 - Prob. 98RECh. 3 - Prob. 99RECh. 3 - Prob. 100RECh. 3 - Prob. 101RECh. 3 - Prob. 102RECh. 3 - Work Determine the work done by a crane lifting an...Ch. 3 - Prob. 104RECh. 3 - Prob. 105RECh. 3 - Prob. 106RECh. 3 - Prob. 107RECh. 3 - Prob. 108RECh. 3 - Prob. 109RECh. 3 - Prob. 110RECh. 3 - Prob. 111RECh. 3 - Prob. 112RECh. 3 - Prob. 113RECh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Prob. 10TCh. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - Prob. 15TCh. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Determine whether the vectors u=6,10 and v=5,3 are...Ch. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 22TCh. 3 - Take this test as you would take a test in class....Ch. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 17CTCh. 3 - Prob. 18CTCh. 3 - Prob. 19CTCh. 3 - Prob. 20CTCh. 3 - Prob. 21CTCh. 3 - Prob. 22CTCh. 3 - Prob. 23CTCh. 3 - Prob. 24CTCh. 3 - Prob. 25CTCh. 3 - Prob. 26CTCh. 3 - Prob. 27CTCh. 3 - Prob. 28CTCh. 3 - Prob. 29CTCh. 3 - Prob. 30CTCh. 3 - Prob. 31CTCh. 3 - Prob. 32CTCh. 3 - Prob. 33CTCh. 3 - Find a unit vector u in the direction of v=i+jCh. 3 - Prob. 35CTCh. 3 - Prob. 36CTCh. 3 - Prob. 37CTCh. 3 - Prob. 38CTCh. 3 - From a point 200 feet from a flagpole, the angles...Ch. 3 - To determine the angle of elevation of a star in...Ch. 3 - Prob. 41CTCh. 3 - Prob. 42CTCh. 3 - Prob. 43CTCh. 3 - Distance In the figure, a beam of light is...Ch. 3 - Prob. 2PSCh. 3 - Locating Lost Hikers A group of hikers is lost in...Ch. 3 - Prob. 4PSCh. 3 - Prob. 5PSCh. 3 - Prob. 6PSCh. 3 - Prob. 7PSCh. 3 - Prob. 8PSCh. 3 - Prob. 9PSCh. 3 - Prob. 10PSCh. 3 - Prob. 13PSCh. 3 - Prob. 14PS
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How to find the magnitude and direction of a given vector; Author: Brian McLogan;https://www.youtube.com/watch?v=4qE-ZrR_NxI;License: Standard YouTube License, CC-BY
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