- 12.1: In Exercises 14, let and Find (a) the component form of the vector ...
- 12.2: In Exercises 14, let and Find (a) the component form of the vector ...
- 12.3: In Exercises 14, let and Find (a) the component form of the vector ...
- 12.4: In Exercises 14, let and Find (a) the component form of the vector ...
- 12.5: In Exercises 58, find the component form of the vector
- 12.6: In Exercises 58, find the component form of the vector
- 12.7: In Exercises 58, find the component form of the vector
- 12.8: In Exercises 58, find the component form of the vector
- 12.9: Express the vectors in Exercises 912 in terms of their lengths and ...
- 12.10: Express the vectors in Exercises 912 in terms of their lengths and ...
- 12.11: Express the vectors in Exercises 912 in terms of their lengths and ...
- 12.12: Express the vectors in Exercises 912 in terms of their lengths and ...
- 12.13: Express the vectors in Exercises 13 and 14 in terms of their length...
- 12.14: Express the vectors in Exercises 13 and 14 in terms of their length...
- 12.15: Find a vector 2 units long in the direction of
- 12.16: Find a vector 5 units long in the direction opposite to the direction
- 12.17: In Exercises 17 and 18, find the angle between v and u, the scalar ...
- 12.18: In Exercises 17 and 18, find the angle between v and u, the scalar ...
- 12.19: In Exercises 19 and 20, find projv u
- 12.20: In Exercises 19 and 20, find projv u
- 12.21: In Exercises 21 and 22, draw coordinate axes and then sketch u, v, ...
- 12.22: In Exercises 21 and 22, draw coordinate axes and then sketch u, v, ...
- 12.23: If and the angle between v and w is find
- 12.24: For what value or values of a will the vectors and be v = -4i - 8j ...
- 12.25: In Exercises 25 and 26, find (a) the area of the parallelogram dete...
- 12.26: In Exercises 25 and 26, find (a) the area of the parallelogram dete...
- 12.27: Suppose that n is normal to a plane and that v is parallel to the p...
- 12.28: Find a vector in the plane parallel to the line
- 12.29: In Exercises 29 and 30, find the distance from the point to the line.
- 12.30: In Exercises 29 and 30, find the distance from the point to the line.
- 12.31: Parametrize the line that passes through the point (1, 2, 3) parall...
- 12.32: Parametrize the line segment joining the points P(1, 2, 0) and
- 12.33: In Exercises 33 and 34, find the distance from the point to the plane.
- 12.34: In Exercises 33 and 34, find the distance from the point to the plane.
- 12.35: Find an equation for the plane that passes through the point normal...
- 12.36: Find an equation for the plane that passes through the point perpen...
- 12.37: In Exercises 37 and 38, find an equation for the plane through poin...
- 12.38: In Exercises 37 and 38, find an equation for the plane through poin...
- 12.39: Find the points in which the line meets the three coordinate planes
- 12.40: Find the point in which the line through the origin perpendicular t...
- 12.41: Find the acute angle between the planes and
- 12.42: Find the acute angle between the planes and
- 12.43: Find parametric equations for the line in which the planes and inte...
- 12.44: Show that the line in which the planes intersect is parallel to the...
- 12.45: The planes and intersect in a line. a. Show that the planes are ort...
- 12.46: Find an equation for the plane that passes through the point (1, 2,...
- 12.47: Is related in any special way to the plane Give reasons for your an...
- 12.48: The equation represents the plane through normal to n. What set doe...
- 12.49: Find the distance from the point P(1, 4, 0) to the plane through A(...
- 12.50: Find the distance from the point (2, 2, 3) to the plane
- 12.51: Find a vector parallel to the plane and orthogonal to
- 12.52: Find a unit vector orthogonal to A in the plane of B and C if
- 12.53: Find a vector of magnitude 2 parallel to the line of intersection o...
- 12.54: Find the point in which the line through the origin perpendicular t...
- 12.55: Find the point in which the line through P(3, 2, 1) normal to the p...
- 12.56: What angle does the line of intersection of the planes and make wit...
- 12.57: The line intersects the plane in a point P. Find the coordinates of...
- 12.58: Show that for every real number k the plane contains the line of in...
- 12.59: Find an equation for the plane through and that lies parallel to th...
- 12.60: Is the line related in any way to the plane Give reasons for your a...
- 12.61: Which of the following are equations for the plane through the poin...
- 12.62: The parallelogram shown here has vertices at and D. Find a. the coo...
- 12.63: Find the distance between the line through the points and and the l...
- 12.64: (Continuation of Exercise 63.) Find the distance between the line t...
- 12.65: Identify and sketch the surfaces in Exercises 6576.
- 12.66: Identify and sketch the surfaces in Exercises 6576.
- 12.67: Identify and sketch the surfaces in Exercises 6576.
- 12.68: Identify and sketch the surfaces in Exercises 6576.
- 12.69: Identify and sketch the surfaces in Exercises 6576.
- 12.70: Identify and sketch the surfaces in Exercises 6576.
- 12.71: Identify and sketch the surfaces in Exercises 6576.
- 12.72: Identify and sketch the surfaces in Exercises 6576.
- 12.73: Identify and sketch the surfaces in Exercises 6576.
- 12.74: Identify and sketch the surfaces in Exercises 6576.
- 12.75: Identify and sketch the surfaces in Exercises 6576.
- 12.76: Identify and sketch the surfaces in Exercises 6576.
Solutions for Chapter 12: Vectors and the Geometry of Space
Full solutions for Thomas' Calculus Early Transcendentals | 12th Edition
ISBN: 9780321588760
Solutions for Chapter 12
20
2
Thomas' Calculus Early Transcendentals was written by and is associated to the ISBN: 9780321588760. This textbook survival guide was created for the textbook: Thomas' Calculus Early Transcendentals, edition: 12. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 12: Vectors and the Geometry of Space includes 76 full step-by-step solutions. Since 76 problems in chapter 12: Vectors and the Geometry of Space have been answered, more than 32979 students have viewed full step-by-step solutions from this chapter.
Key Calculus Terms and definitions covered in this textbook
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Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)
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Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x ) - x 2)2 + (y1 - y2)2 + (z 1 - z 2)2
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Distance (on a number line)
The distance between real numbers a and b, or |a - b|
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Frequency table (in statistics)
A table showing frequencies.
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Future value of an annuity
The net amount of money returned from an annuity.
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Hypotenuse
Side opposite the right angle in a right triangle.
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Integrable over [a, b] Lba
ƒ1x2 dx exists.
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Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative
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Linear regression
A procedure for finding the straight line that is the best fit for the data
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NDER ƒ(a)
See Numerical derivative of ƒ at x = a.
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Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle
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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.
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Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.
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Quotient rule of logarithms
logb a R S b = logb R - logb S, R > 0, S > 0
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Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.
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Terminal point
See Arrow.
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Terms of a sequence
The range elements of a sequence.
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Third quartile
See Quartile.
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Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.
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Vertical line
x = a.