 12.5.1: Determine whether each statement is true or false. (a) Two lines pa...
 12.5.2: Find a vector equation and parametric equations for the line.The li...
 12.5.3: Find a vector equation and parametric equations for the line.The li...
 12.5.4: Find a vector equation and parametric equations for the line.The li...
 12.5.5: Find a vector equation and parametric equations for the line.The li...
 12.5.6: Find parametric equations and symmetric equations for the line. The...
 12.5.7: Find parametric equations and symmetric equations for the line. The...
 12.5.8: Find parametric equations and symmetric equations for the line. The...
 12.5.9: Find parametric equations and symmetric equations for the line. The...
 12.5.10: Find parametric equations and symmetric equations for the line. The...
 12.5.11: Find parametric equations and symmetric equations for the line. The...
 12.5.12: Find parametric equations and symmetric equations for the line. The...
 12.5.13: Is the line through and parallel to the line through and ?
 12.5.14: Is the line through and perpendicular to the line through and ?
 12.5.15: (a) Find symmetric equations for the line that passes through the p...
 12.5.16: (a) Find parametric equations for the line through that is perpendi...
 12.5.17: Find a vector equation for the line segment from to .
 12.5.18: Find parametric equations for the line segment from to .
 12.5.19: Determine whether the lines and are parallel, skew, or intersecting...
 12.5.20: Determine whether the lines and are parallel, skew, or intersecting...
 12.5.21: Determine whether the lines and are parallel, skew, or intersecting...
 12.5.22: Determine whether the lines and are parallel, skew, or intersecting...
 12.5.23: Find an equation of the plane. The plane through the origin and per...
 12.5.24: Find an equation of the plane. The plane through the point and with...
 12.5.25: Find an equation of the plane. The plane through the point and with...
 12.5.26: Find an equation of the plane. The plane through the point and perp...
 12.5.27: Find an equation of the plane. The plane through the point and para...
 12.5.28: Find an equation of the plane. The plane through the point and para...
 12.5.29: Find an equation of the plane. The plane through the point and para...
 12.5.30: Find an equation of the plane. The plane that contains the line , ,...
 12.5.31: Find an equation of the plane. The plane through the points , , and
 12.5.32: Find an equation of the plane. The plane through
 12.5.33: Find an equation of the plane. The plane through the points , , and
 12.5.34: Find an equation of the plane. The plane that passes through the po...
 12.5.35: Find an equation of the plane. The plane that passes through the po...
 12.5.36: Find an equation of the plane. The plane that passes through the po...
 12.5.37: Find an equation of the plane. The plane that passes through the po...
 12.5.38: Find an equation of the plane. The plane that passes through the po...
 12.5.39: Find an equation of the plane. The plane that passes through the po...
 12.5.40: Find an equation of the plane. The plane that passes through the li...
 12.5.41: Use intercepts to help sketch the plane. 2x 5y z 10
 12.5.42: Use intercepts to help sketch the plane. 3x y 2z 6
 12.5.43: Use intercepts to help sketch the plane. 6x 3y 4z 6
 12.5.44: Use intercepts to help sketch the plane. 6x 5y 3z 15
 12.5.45: Find the point at which the line intersects the given plane. x 3 t ...
 12.5.46: Find the point at which the line intersects the given plane. x 1 2t...
 12.5.47: Find the point at which the line intersects the given plane. x y 1 ...
 12.5.48: Where does the line through and intersect the plane ?
 12.5.49: Find direction numbers for the line of intersection of the planes a...
 12.5.50: Find the cosine of the angle between the planes and
 12.5.51: Determine whether the planes are parallel, perpendicular, or neithe...
 12.5.52: Determine whether the planes are parallel, perpendicular, or neithe...
 12.5.53: Determine whether the planes are parallel, perpendicular, or neithe...
 12.5.54: Determine whether the planes are parallel, perpendicular, or neithe...
 12.5.55: Determine whether the planes are parallel, perpendicular, or neithe...
 12.5.56: Determine whether the planes are parallel, perpendicular, or neithe...
 12.5.57: (a) Find parametric equations for the line of intersection of the p...
 12.5.58: (a) Find parametric equations for the line of intersection of the p...
 12.5.59: Find symmetric equations for the line of intersection of the planes...
 12.5.60: Find symmetric equations for the line of intersection of the planes...
 12.5.61: Find an equation for the plane consisting of all points that are eq...
 12.5.62: Find an equation for the plane consisting of all points that are eq...
 12.5.63: Find an equation of the plane with intercept , intercept , and i...
 12.5.64: (a) Find the point at which the given lines intersect: (b) Find an ...
 12.5.65: Find parametric equations for the line through the point that is pa...
 12.5.66: Find parametric equations for the line through the point that is pe...
 12.5.67: Which of the following four planes are parallel? Are any of them id...
 12.5.68: Which of the following four lines are parallel? Are any of them ide...
 12.5.69: Use the formula in Exercise 45 in Section 12.4 to find the distance...
 12.5.70: Use the formula in Exercise 45 in Section 12.4 to find the distance...
 12.5.71: Find the distance from the point to the given plane. 1, 2, 4 3x 2y ...
 12.5.72: Find the distance from the point to the given plane. 6, 3, 5 x 2y 4z 8
 12.5.73: Find the distance between the given parallel planes. 2x 3y z 4 4x 6...
 12.5.74: Find the distance between the given parallel planes. 6z 4y 2x 9z 1 ...
 12.5.75: Show that the distance between the parallel planes and is
 12.5.76: Find equations of the planes that are parallel to the plane and two...
 12.5.77: Show that the lines with symmetric equations and are skew, and find...
 12.5.78: Find the distance between the skew lines with parametric equations ...
 12.5.79: Let be the line through the origin and the point . Let be the line ...
 12.5.80: Let be the line through the points and . Let be the line of interse...
 12.5.81: If , , and are not all 0, show that the equation represents a plane...
 12.5.82: Give a geometric description of each family of planes.
Solutions for Chapter 12.5: EQUATIONS OF LINES AND PLANES
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 12.5: EQUATIONS OF LINES AND PLANES
Get Full SolutionsSince 82 problems in chapter 12.5: EQUATIONS OF LINES AND PLANES have been answered, more than 16143 students have viewed full stepbystep solutions from this chapter. Chapter 12.5: EQUATIONS OF LINES AND PLANES includes 82 full stepbystep solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879.

Compound interest
Interest that becomes part of the investment

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

Focus, foci
See Ellipse, Hyperbola, Parabola.

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

Horizontal line
y = b.

Hypotenuse
Side opposite the right angle in a right triangle.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Intercepted arc
Arc of a circle between the initial side and terminal side of a central angle.

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Order of an m x n matrix
The order of an m x n matrix is m x n.

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Partial sums
See Sequence of partial sums.

Real zeros
Zeros of a function that are real numbers.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Solve a system
To find all solutions of a system.

Unbounded interval
An interval that extends to ? or ? (or both).

Union of two sets A and B
The set of all elements that belong to A or B or both.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Venn diagram
A visualization of the relationships among events within a sample space.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.