 11.1.1: ?In Exercises 1–4, (a) find the component form of the vector v and ...
 11.1.2: ?In Exercises 1–4, (a) find the component form of the vector v and ...
 11.1.3: ?In Exercises 1–4, (a) find the component form of the vector v and ...
 11.1.4: ?In Exercises 1–4, (a) find the component form of the vector v and ...
 11.1.5: ?In Exercises 58, find the vectors u and v whose initial and termi...
 11.1.6: ?In Exercises 58, find the vectors u and v whose initial and termi...
 11.1.7: ?In Exercises 58, find the vectors u and v whose initial and termi...
 11.1.8: ?In Exercises 58, find the vectors u and v whose initial and termi...
 11.1.9: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.10: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.11: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.12: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.13: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.14: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.15: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.16: ?In Exercises 916, the initial and terminal points of a vector v a...
 11.1.17: ?In Exercises 17 and 18 , sketch each scalar multiple of v.\(\mathb...
 11.1.18: ?In Exercises 17 and 18 , sketch each scalar multiple of v.\(\mathb...
 11.1.19: ?In Exercises 19 and 20, find (a) \(\frac{2}{3} u\), (b) 3v, (c) v ...
 11.1.20: ?In Exercises 19 and 20, find (a) \(\frac{2}{3} u\), (b) 3v, (c) v ...
 11.1.21: ?In Exercises 2126, use the figure to sketch a graph of the vector...
 11.1.22: ?In Exercises 2126, use the figure to sketch a graph of the vector...
 11.1.23: ?In Exercises 2126, use the figure to sketch a graph of the vector...
 11.1.24: ?In Exercises 2126, use the figure to sketch a graph of the vector...
 11.1.25: ?In Exercises 2126, use the figure to sketch a graph of the vector...
 11.1.26: ?In Exercises 2126, use the figure to sketch a graph of the vector...
 11.1.27: ?In Exercises 27 and 28 , the vector v and its initial point are gi...
 11.1.28: ?In Exercises 27 and 28 , the vector v and its initial point are gi...
 11.1.29: ?In Exercises 2934, find the magnitude of v.v = 7i
 11.1.30: ?In Exercises 2934, find the magnitude of v.v = 3i
 11.1.31: ?In Exercises 2934, find the magnitude of v.\(\mathbf{v}=\langle 4...
 11.1.32: ?In Exercises 2934, find the magnitude of v.\(\mathbf{v}=\langle 1...
 11.1.33: ?In Exercises 2934, find the magnitude of v.v = 6i  5j
 11.1.34: ?In Exercises 2934, find the magnitude of v.v = 10i + 3j
 11.1.35: ?In Exercises 3538, find the unit vector in the direction of v and...
 11.1.36: ?In Exercises 3538, find the unit vector in the direction of v and...
 11.1.37: ?In Exercises 3538, find the unit vector in the direction of v and...
 11.1.38: ?In Exercises 3538, find the unit vector in the direction of v and...
 11.1.39: ?In Exercises 3942, find the following.(a) u(b) v(c) u +...
 11.1.40: ?In Exercises 3942, find the following.(a) u(b) v(c) u +...
 11.1.41: ?In Exercises 3942, find the following.(a) u(b) v(c) u +...
 11.1.42: ?In Exercises 3942, find the following.(a) u(b) v(c) u +...
 11.1.43: ?In Exercises 43 and 44 , sketch a graph of u, v, and u + v. Then d...
 11.1.44: ?In Exercises 43 and 44 , sketch a graph of u, v, and u + v. Then d...
 11.1.45: ?In Exercises 4548, find the vector v with the given magnitude and...
 11.1.46: ?In Exercises 4548, find the vector v with the given magnitude and...
 11.1.47: ?In Exercises 4548, find the vector v with the given magnitude and...
 11.1.48: ?In Exercises 4548, find the vector v with the given magnitude and...
 11.1.49: ?In Exercises 4952, find the component form of v given its magnitu...
 11.1.50: ?In Exercises 4952, find the component form of v given its magnitu...
 11.1.51: ?In Exercises 4952, find the component form of v given its magnitu...
 11.1.52: ?In Exercises 4952, find the component form of v given its magnitu...
 11.1.53: ?In Exercises 5356, find the component form of u + v given the len...
 11.1.54: ?In Exercises 5356, find the component form of u + v given the len...
 11.1.55: ?In Exercises 5356, find the component form of u + v given the len...
 11.1.56: ?In Exercises 5356, find the component form of u + v given the len...
 11.1.57: Scalar and Vector In your own words, state the difference between a...
 11.1.58: ?Identify the quantity as a scalar or as a vector. Explain your rea...
 11.1.59: ?Three vertices of a parallelogram are (1, 2), (3, 1), and (8, 4). ...
 11.1.60: ?Use the figure to determine whether each statement is true or fals...
 11.1.61: ?In Exercises 6166, find a and b such that v = au + bw, where \(\m...
 11.1.62: ?In Exercises 6166, find a and b such that v = au + bw, where \(\m...
 11.1.63: ?In Exercises 6166, find a and b such that v = au + bw, where \(\m...
 11.1.64: ?In Exercises 6166, find a and b such that v = au + bw, where \(\m...
 11.1.65: ?In Exercises 6166, find a and b such that v = au + bw, where \(\m...
 11.1.66: ?In Exercises 6166, find a and b such that v = au + bw, where \(\m...
 11.1.67: ?In Exercises 6772, find a unit vector (a) parallel to and (b) per...
 11.1.68: ?In Exercises 6772, find a unit vector (a) parallel to and (b) per...
 11.1.69: ?In Exercises 6772, find a unit vector (a) parallel to and (b) per...
 11.1.70: ?In Exercises 6772, find a unit vector (a) parallel to and (b) per...
 11.1.71: ?In Exercises 6772, find a unit vector (a) parallel to and (b) per...
 11.1.72: ?In Exercises 6772, find a unit vector (a) parallel to and (b) per...
 11.1.73: ?In Exercises 73 and 74, find the component form of v given the mag...
 11.1.74: ?In Exercises 73 and 74, find the component form of v given the mag...
 11.1.75: ?Forces with magnitudes of 500 pounds and 200 pounds act on a machi...
 11.1.76: ?Forces with magnitudes of 180 newtons and 275 newtons act on a hoo...
 11.1.77: ?Three forces with magnitudes of 75 pounds, 100 pounds, and 125 pou...
 11.1.78: ?Three forces with magnitudes of 400 newtons, 280 newtons, and 350 ...
 11.1.79: Think About It Consider two forces of equal magnitude acting on a p...
 11.1.80: ?Determine the tension in each cable supporting the given load for ...
 11.1.81: ?A gun with a muzzle velocity of 1200 feet per second is fired at a...
 11.1.82: ?To carry a 100pound cylindrical weight, two workers lift on the e...
 11.1.83: ?A plane is flying with a bearing of \(302^{\circ}\). Its speed wit...
 11.1.84: ?A plane flies at a constant groundspeed of 400 miles per hour due ...
 11.1.85: ?In Exercises 8590, determine whether the statement is true or fal...
 11.1.86: ?In Exercises 8590, determine whether the statement is true or fal...
 11.1.87: ?In Exercises 8590, determine whether the statement is true or fal...
 11.1.88: ?In Exercises 8590, determine whether the statement is true or fal...
 11.1.89: ?In Exercises 8590, determine whether the statement is true or fal...
 11.1.90: ?In Exercises 8590, determine whether the statement is true or fal...
 11.1.91: ?Prove that \(\mathbf{u}=(\cos \theta) \mathbf{i}(\sin \theta) \ma...
 11.1.92: Geometry Using vectors, prove that the line segment joining the mid...
 11.1.93: Geometry Using vectors, prove that the diagonals of a parallelogram...
 11.1.94: ?Prove that the vector w = uv + vu bisects the angle betwee...
 11.1.95: ?Consider the vector \(\mathbf{u}=\langle x, y\rangle\). Describe t...
 11.1.96: ?A coast artillery gun can fire at any angle of elevation between \...
Solutions for Chapter 11.1: Vectors in the Plane
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 11.1: Vectors in the Plane
Get Full SolutionsChapter 11.1: Vectors in the Plane includes 96 full stepbystep solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. This expansive textbook survival guide covers the following chapters and their solutions. Since 96 problems in chapter 11.1: Vectors in the Plane have been answered, more than 184409 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6.

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Differentiable at x = a
ƒ'(a) exists

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Leading coefficient
See Polynomial function in x

Natural numbers
The numbers 1, 2, 3, . . . ,.

Negative numbers
Real numbers shown to the left of the origin on a number line.

nth root of unity
A complex number v such that vn = 1

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Parameter interval
See Parametric equations.

Positive association
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Real axis
See Complex plane.

Scatter plot
A plot of all the ordered pairs of a twovariable data set on a coordinate plane.

Stem
The initial digit or digits of a number in a stemplot.

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

Zoom out
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).