 1.5.1: Calculate an equation for the plane containing the point (3, 1, 2) ...
 1.5.2: Find an equation for the plane containing the point (9, 5, 1) and p...
 1.5.3: Find an equation for the plane containing the points (3, 1, 2), (2,...
 1.5.4: Find an equation for the plane containing the points (A, 0, 0), (0,...
 1.5.5: Give an equation for the plane that is parallel to the plane 5x 4y ...
 1.5.6: Give an equation for the plane parallel to the plane 2x 3y + z = 5 ...
 1.5.7: Find an equation for the plane parallel to the plane x y + 7z = 10 ...
 1.5.8: Give an equation for the plane parallel to the plane 2x + 2y + z = ...
 1.5.9: Explain why there is no plane parallel to the plane 5x 3y + 2z = 10...
 1.5.10: Find an equation for the plane that contains the line x = 2t 1, y =...
 1.5.11: Find an equation for the plane that is perpendicular to the line x ...
 1.5.12: Find an equation for the plane that contains the two linesl1: x = t...
 1.5.13: Give a set of parametric equations for the line of intersection of ...
 1.5.14: Give a set of parametric equations for the line through (5, 0, 6) t...
 1.5.15: Find a value for A so that the planes 8x 6y + 9Az = 6 and Ax + y + ...
 1.5.16: Find values for A so that the planes Ax y + z = 1 and 3Ax + Ay 2z =...
 1.5.17: Give a set of parametric equations for each of the planes described...
 1.5.18: Give a set of parametric equations for each of the planes described...
 1.5.19: Give a set of parametric equations for each of the planes described...
 1.5.20: Give a set of parametric equations for each of the planes described...
 1.5.21: Give a set of parametric equations for each of the planes described...
 1.5.22: Give a set of parametric equations for each of the planes described...
 1.5.23: Find a single equation of the form Ax + By + C z = D that describes...
 1.5.24: Find the distance between the point (1, 2, 3) and the line l: x = 2...
 1.5.25: Find the distance between the point (2, 1) and the line l: x = 3t +...
 1.5.26: Find the distance between the point (11, 10, 20) and the line l: x ...
 1.5.27: Determine the distance between the two lines l1(t) = t(8, 1, 0) + (...
 1.5.28: Compute the distance between the two lines l1(t) = (t 7)i + (5t + 1...
 1.5.29: (a) Find the distance between the two lines l1(t) = t(3, 1, 2) + (4...
 1.5.30: (a) The lines l1(t) = t(1, 1, 5) + (2, 0, 4) and l2(t) = t(1, 1, 5)...
 1.5.31: Find the distance between the two planes given by the equations x 3...
 1.5.32: Calculate the distance between the two planes 5x 2y + 2z = 12 and 1...
 1.5.33: Show that the distance d between the two parallel planes determined...
 1.5.34: Two planes are given parametrically by the vector equations x1(s, t...
 1.5.35: Write equations for the planes that are parallel to x + 3y 5z = 2 a...
 1.5.36: Suppose that l1(t) = ta + b1 and l2(t) = ta + b2 are parallel lines...
 1.5.37: Let be the plane in R3 with normal vector n that passes through the...
 1.5.38: Show that the distance D between parallel planes with normal vector...
 1.5.39: Suppose that l1(t) = ta1 + b1 and l2(t) = ta2 + b2 are skew lines i...
Solutions for Chapter 1.5: Equations for Planes; Distance Problems
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 1.5: Equations for Planes; Distance Problems
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Chapter 1.5: Equations for Planes; Distance Problems includes 39 full stepbystep solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Since 39 problems in chapter 1.5: Equations for Planes; Distance Problems have been answered, more than 12803 students have viewed full stepbystep solutions from this chapter.

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Conversion factor
A ratio equal to 1, used for unit conversion

Cosine
The function y = cos x

Determinant
A number that is associated with a square matrix

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Distributive property
a(b + c) = ab + ac and related properties

Explanatory variable
A variable that affects a response variable.

Function
A relation that associates each value in the domain with exactly one value in the range.

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.

Measure of an angle
The number of degrees or radians in an angle

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Parametric curve
The graph of parametric equations.

Phase shift
See Sinusoid.

Positive angle
Angle generated by a counterclockwise rotation.

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Slant asymptote
An end behavior asymptote that is a slant line

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Transpose of a matrix
The matrix AT obtained by interchanging the rows and columns of A.