 12.5.1: Determine whether each statement is true or false. (a) Two lines pa...
 12.5.2: 25 Find a vector equation and parametric equations for the line.The...
 12.5.3: 25 Find a vector equation and parametric equations for the line.The...
 12.5.4: 25 Find a vector equation and parametric equations for the line.The...
 12.5.5: 25 Find a vector equation and parametric equations for the line.The...
 12.5.6: 612 Find parametric equations and symmetric equations for the line....
 12.5.7: 612 Find parametric equations and symmetric equations for the line....
 12.5.8: 612 Find parametric equations and symmetric equations for the line....
 12.5.9: 612 Find parametric equations and symmetric equations for the line....
 12.5.10: 612 Find parametric equations and symmetric equations for the line....
 12.5.11: 612 Find parametric equations and symmetric equations for the line....
 12.5.12: 612 Find parametric equations and symmetric equations for the line....
 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: 1922 Determine whether the lines and are parallel, skew, or interse...
 12.5.20: 1922 Determine whether the lines and are parallel, skew, or interse...
 12.5.21: 1922 Determine whether the lines and are parallel, skew, or interse...
 12.5.22: 1922 Determine whether the lines and are parallel, skew, or interse...
 12.5.23: 23 40 Find an equation of the plane.The plane through the origin an...
 12.5.24: 23 40 Find an equation of the plane.The plane through the point and...
 12.5.25: 23 40 Find an equation of the plane.The plane through the point and...
 12.5.26: 23 40 Find an equation of the plane.The plane through the point and...
 12.5.27: 23 40 Find an equation of the plane.The plane through the point and...
 12.5.28: 23 40 Find an equation of the plane.The plane through the point and...
 12.5.29: 23 40 Find an equation of the plane.The plane through the point and...
 12.5.30: 23 40 Find an equation of the plane.. The plane that contains the l...
 12.5.31: 23 40 Find an equation of the plane.The plane through the points ,
 12.5.32: 23 40 Find an equation of the plane.The plane through the origin an...
 12.5.33: 23 40 Find an equation of the plane.The plane through the points , ...
 12.5.34: 23 40 Find an equation of the plane.The plane that passes through t...
 12.5.35: 23 40 Find an equation of the plane.The plane that passes through t...
 12.5.36: 23 40 Find an equation of the plane.The plane that passes through t...
 12.5.37: 23 40 Find an equation of the plane.The plane that passes through t...
 12.5.38: 23 40 Find an equation of the plane.The plane that passes through t...
 12.5.39: 23 40 Find an equation of the plane.The plane that passes through t...
 12.5.40: 23 40 Find an equation of the plane.The plane that passes through t...
 12.5.41: 41 44 Use intercepts to help sketch the plane.2x 5y z 10 3x
 12.5.42: 41 44 Use intercepts to help sketch the plane.3x y 2z 66x
 12.5.43: 41 44 Use intercepts to help sketch the plane.6x 3y 4z 6 6x
 12.5.44: 41 44 Use intercepts to help sketch the plane.6x 5y 3z 15x
 12.5.45: 45 47 Find the point at which the line intersects the given plane.x...
 12.5.46: 45 47 Find the point at which the line intersects the given plane.x...
 12.5.47: 45 47 Find the point at which the line intersects the given plane.x...
 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
 12.5.50: Find the cosine of the angle between the planes and
 12.5.51: 5156 Determine whether the planes are parallel, perpendicular, or n...
 12.5.52: 5156 Determine whether the planes are parallel, perpendicular, or n...
 12.5.53: 5156 Determine whether the planes are parallel, perpendicular, or n...
 12.5.54: 5156 Determine whether the planes are parallel, perpendicular, or n...
 12.5.55: 5156 Determine whether the planes are parallel, perpendicular, or n...
 12.5.56: 5156 Determine whether the planes are parallel, perpendicular, or n...
 12.5.57: 5758 (a) Find parametric equations for the line of intersection of ...
 12.5.58: 5758 (a) Find parametric equations for the line of intersection of ...
 12.5.59: 5960 Find symmetric equations for the line of intersection of the p...
 12.5.60: 5960 Find symmetric equations for the line of intersection of the p...
 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 ...
 12.5.63: . Find an equation of the plane with intercept , intercept , and ...
 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: 6970 Use the formula in Exercise 45 in Section 12.4 to find the dis...
 12.5.70: 6970 Use the formula in Exercise 45 in Section 12.4 to find the dis...
 12.5.71: 7172 Find the distance from the point to the given plane.1, 2, 4 3x...
 12.5.72: 7172 Find the distance from the point to the given plane.6, 3, 5 x ...
 12.5.73: 7374 Find the distance between the given parallel planes.2x 3y z 4 ...
 12.5.74: 7374 Find the distance between the given parallel planes.6z 4y 2x 9...
 12.5.75: Show that the distance between the parallel planes and isD d1 d2 sa...
 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 pla...
 12.5.82: Give a geometric description of each family of planes.x y z c x y c...
Solutions for Chapter 12.5: Equations of Lines and Planes
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
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 29454 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 12.5: Equations of Lines and Planes includes 82 full stepbystep solutions.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Common ratio
See Geometric sequence.

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Distance (on a number line)
The distance between real numbers a and b, or a  b

Exponent
See nth power of a.

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

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

Ordered pair
A pair of real numbers (x, y), p. 12.

Pole
See Polar coordinate system.

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Real axis
See Complex plane.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

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

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.

xintercept
A point that lies on both the graph and the xaxis,.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.

zaxis
Usually the third dimension in Cartesian space.

Zero matrix
A matrix consisting entirely of zeros.