 6.3.1: Fill in the blanks. A ________ ________ ________ can be used to rep...
 6.3.2: Fill in the blanks. The directed line segment has ________ point an...
 6.3.3: Fill in the blanks. The ________ of the directed line segment is de...
 6.3.4: Fill in the blanks. The set of all directed line segments that are ...
 6.3.5: Fill in the blanks. In order to show that two vectors are equivalen...
 6.3.6: Fill in the blanks. The directed line segment whose initial point i...
 6.3.7: Fill in the blanks. A vector that has a magnitude of 1 is called a ...
 6.3.8: Fill in the blanks. The two basic vector operations are scalar ____...
 6.3.9: Fill in the blanks. The vector is called the ________ of vector add...
 6.3.10: Fill in the blanks. The vector sum is called a ________ ________ of...
 6.3.11: Showing That Two Vectors Are Equivalent In Exercises 11 and 12, sho...
 6.3.12: Showing That Two Vectors Are Equivalent In Exercises 11 and 12, sho...
 6.3.13: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.14: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.15: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.16: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.17: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.18: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.19: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.20: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.21: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.22: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.23: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.24: Finding the Component Form of a Vector In Exercises 1324, find the ...
 6.3.25: Sketching the Graph of a Vector In Exercises 2530, use the figure t...
 6.3.26: Sketching the Graph of a Vector In Exercises 2530, use the figure t...
 6.3.27: Sketching the Graph of a Vector In Exercises 2530, use the figure t...
 6.3.28: Sketching the Graph of a Vector In Exercises 2530, use the figure t...
 6.3.29: Sketching the Graph of a Vector In Exercises 2530, use the figure t...
 6.3.30: Sketching the Graph of a Vector In Exercises 2530, use the figure t...
 6.3.31: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.32: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.33: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.34: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.35: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.36: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.37: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.38: Vector Operations In Exercises 3138, find (a) (b) and (c) Then sket...
 6.3.39: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.40: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.41: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.42: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.43: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.44: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.45: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.46: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.47: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.48: Finding a Unit Vector In Exercises 39 48, find a unit vector in the...
 6.3.49: Finding a Vector In Exercises 4952, find the vector v with the give...
 6.3.50: Finding a Vector In Exercises 4952, find the vector v with the give...
 6.3.51: Finding a Vector In Exercises 4952, find the vector v with the give...
 6.3.52: Finding a Vector In Exercises 4952, find the vector v with the give...
 6.3.53: Writing a Linear Combination of Unit Vectors In Exercises 5356, the...
 6.3.54: Writing a Linear Combination of Unit Vectors In Exercises 5356, the...
 6.3.55: Writing a Linear Combination of Unit Vectors In Exercises 5356, the...
 6.3.56: Writing a Linear Combination of Unit Vectors In Exercises 5356, the...
 6.3.57: 56. Vector Operations In Exercises 5762, find the component form of...
 6.3.58: 56. Vector Operations In Exercises 5762, find the component form of...
 6.3.59: 56. Vector Operations In Exercises 5762, find the component form of...
 6.3.60: 56. Vector Operations In Exercises 5762, find the component form of...
 6.3.61: 56. Vector Operations In Exercises 5762, find the component form of...
 6.3.62: 56. Vector Operations In Exercises 5762, find the component form of...
 6.3.63: Finding the Direction Angle of a Vector In Exercises 6366, find the...
 6.3.64: Finding the Direction Angle of a Vector In Exercises 6366, find the...
 6.3.65: Finding the Direction Angle of a Vector In Exercises 6366, find the...
 6.3.66: Finding the Direction Angle of a Vector In Exercises 6366, find the...
 6.3.67: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.68: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.69: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.70: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.71: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.72: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.73: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.74: Finding the Component Form of a Vector In Exercises 6774, find the ...
 6.3.75: Finding the Component Form of a Vector In Exercises 7578, find the ...
 6.3.76: Finding the Component Form of a Vector In Exercises 7578, find the ...
 6.3.77: Finding the Component Form of a Vector In Exercises 7578, find the ...
 6.3.78: Finding the Component Form of a Vector In Exercises 7578, find the ...
 6.3.79: Using the Law of Cosines In Exercises 79 and 80, use the Law of Cos...
 6.3.80: Using the Law of Cosines In Exercises 79 and 80, use the Law of Cos...
 6.3.81: Resultant Force In Exercises 81 and 82, find the angle between the ...
 6.3.82: Resultant Force In Exercises 81 and 82, find the angle between the ...
 6.3.83: Velocity A gun with a muzzle velocity of 1200 feet per second is fi...
 6.3.84: Velocity Pitcher Joel Zumaya was recorded throwing a pitch at a vel...
 6.3.85: Resultant Force Forces with magnitudes of 125 newtons and 300 newto...
 6.3.86: Resultant Force Forces with magnitudes of 2000 newtons and 900 newt...
 6.3.87: Resultant Force Three forces with magnitudes of 75 pounds, 100 poun...
 6.3.88: Resultant Force Three forces with magnitudes of 70 pounds, 40 pound...
 6.3.89: Cable Tension The cranes shown in the figure are lifting an object ...
 6.3.90: Cable Tension Repeat Exercise 89 for and
 6.3.91: Cable Tension In Exercises 91 and 92, use the figure to determine t...
 6.3.92: Cable Tension In Exercises 91 and 92, use the figure to determine t...
 6.3.93: Tow Line Tension A loaded barge is being towed by two tugboats, and...
 6.3.94: Rope Tension To carry a 100pound cylindrical weight, two people li...
 6.3.95: Find when pounds and
 6.3.96: Find when pounds and
 6.3.97: Find when pounds and pounds.
 6.3.98: Find when pounds and
 6.3.99: Work A heavy object is pulled 30 feet across a floor, using a force...
 6.3.100: Rope Tension A tetherball weighing 1 pound is pulled outward from t...
 6.3.101: Navigation An airplane is flying in the direction of with an airspe...
 6.3.102: Navigation A commercial jet is flying from Miami to Seattle. The je...
 6.3.103: True or False? In Exercises 103106, determine whether the statement...
 6.3.104: True or False? In Exercises 103106, determine whether the statement...
 6.3.105: True or False? In Exercises 103106, determine whether the statement...
 6.3.106: True or False? In Exercises 103106, determine whether the statement...
 6.3.107: Proof Prove that is a unit vector for any value of
 6.3.108: Technology Write a program for your graphing utility that graphs tw...
 6.3.109: Finding the Difference of Two Vectors In Exercises 109 and 110, use...
 6.3.110: Finding the Difference of Two Vectors In Exercises 109 and 110, use...
 6.3.111: Graphical Reasoning Consider two forces (a) Find as a function of (...
 6.3.112: HOW DO YOU SEE IT? Use the figure to determine whether each stateme...
 6.3.113: Writing Give geometric descriptions of the operations of addition o...
 6.3.114: Writing Identify the quantity as a scalar or as a vector. Explain y...
Solutions for Chapter 6.3: Vectors in the Plane
Full solutions for Precalculus with Limits  3rd Edition
ISBN: 9781133947202
Solutions for Chapter 6.3: Vectors in the Plane
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus with Limits, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus with Limits was written by and is associated to the ISBN: 9781133947202. Chapter 6.3: Vectors in the Plane includes 114 full stepbystep solutions. Since 114 problems in chapter 6.3: Vectors in the Plane have been answered, more than 34648 students have viewed full stepbystep solutions from this chapter.

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Base
See Exponential function, Logarithmic function, nth power of a.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Closed interval
An interval that includes its endpoints

Continuous function
A function that is continuous on its entire domain

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Implied domain
The domain of a function’s algebraic expression.

Instantaneous velocity
The instantaneous rate of change of a position function with respect to time, p. 737.

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Parametrization
A set of parametric equations for a curve.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Reciprocal function
The function ƒ(x) = 1x

Secant line of ƒ
A line joining two points of the graph of ƒ.