 12.1: (a) Find an equation of the sphere that passes through the point an...
 12.2: Copy the vectors in the figure and use them to draw each of the fol...
 12.3: If u and v are the vectors shown in the figure, find and . Is u v d...
 12.4: Calculate the given quantity if a i j 2kb 3i 2j kc j 5k2a 3b b a b ...
 12.5: Find the values of such that the vectors and are orthogonal.
 12.6: Find two unit vectors that are orthogonal to both and .
 12.7: Suppose that . Find
 12.8: Show that if , , and are in , then
 12.9: Find the acute angle between two diagonals of a cube.
 12.10: Given the points , , , and , find the volume of the parallelepiped ...
 12.11: (a) Find a vector perpendicular to the plane through the points , ,...
 12.12: A constant force moves an object along the line segment from to . F...
 12.13: A boat is pulled onto shore using two ropes, as shown in the diagra...
 12.14: Find the magnitude of the torque about if a 50N force is applied a...
 12.15: Find parametric equations for the line.The line through 4, 1, 2 1, ...
 12.16: Find parametric equations for the line.The line through 1, 0, 1 1 3...
 12.17: Find parametric equations for the line.The line through 2, 2, 4 2x ...
 12.18: Find an equation of the plane.The plane through 2, 1, 0 x 4y 3z 1 3,
 12.19: Find an equation of the plane.The plane through 3, 1, 1 4, 0, 2 6, ...
 12.20: Find an equation of the plane.The plane through 1, 2, 2 x 2t y 3 t ...
 12.21: Find the point in which the line with parametric equations , , inte...
 12.22: Find the distance from the origin to the line
 12.23: Determine whether the lines given by the symmetric equations and ar...
 12.24: (a) Show that the planes and are neither parallel nor perpendicular...
 12.25: Find an equation of the plane through the line of intersection of t...
 12.26: (a) Find an equation of the plane that passes through the points , ...
 12.27: Find the distance between the planes and
 12.28: Identify and sketch the graph of each surface.
 12.29: Identify and sketch the graph of each surface.
 12.30: Identify and sketch the graph of each surface.
 12.31: Identify and sketch the graph of each surface.
 12.32: Identify and sketch the graph of each surface.
 12.33: Identify and sketch the graph of each surface.
 12.34: Identify and sketch the graph of each surface.
 12.35: Identify and sketch the graph of each surface.
 12.36: Identify and sketch the graph of each surface.
 12.37: An ellipsoid is created by rotating the ellipse about the axis. Fi...
 12.38: A surface consists of all points such that the distance from to the...
Solutions for Chapter 12: Calculus, 7th Edition
Full solutions for Calculus,  7th Edition
ISBN: 9780538497817
Solutions for Chapter 12
Get Full SolutionsChapter 12 includes 38 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus, was written by and is associated to the ISBN: 9780538497817. This textbook survival guide was created for the textbook: Calculus,, edition: 7. Since 38 problems in chapter 12 have been answered, more than 7552 students have viewed full stepbystep solutions from this chapter.

Acute angle
An angle whose measure is between 0° and 90°

Arccosine function
See Inverse cosine function.

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

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Compound interest
Interest that becomes part of the investment

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

End behavior asymptote of a rational function
A polynomial that the function approaches as.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Multiplicative inverse of a matrix
See Inverse of a matrix

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

Order of magnitude (of n)
log n.

Range of a function
The set of all output values corresponding to elements in the domain.

Reciprocal function
The function ƒ(x) = 1x

Xmax
The xvalue of the right side of the viewing window,.