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Math
Calculus
Calculus, Early Transcendentals
Chapter 12.3, Problem 66E
Chapter 12.3, Problem 66E
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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12.1 Three-dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Equations Of Lines And Planes
12.6 Cylinders And Quadric Surfaces
Chapter Questions
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Problem 1E: Which of the following expressions are meaningful? Which are meaningless? Explain. (a) (a b) c (b)...
Problem 2E: Find a b. 2. a = 5, 2, b = 3, 4
Problem 3E: Find a b. 3. a = 1.5, 0.4, b = 4, 6
Problem 4E: Find a b. 4. a = 6, 2, 3, b = 2, 5, 1
Problem 5E: Find a b. 5. a = 4, 1, 14, b = 6, 3, 8
Problem 6E: Find a b. 6. a. = p, p, 2p, b = 2q, q, q
Problem 7E: Find a b. 7. a = 2i + j, b = i j + k
Problem 8E: Find a b. 8. a = 3i + 2j k, b = 4i + 5k
Problem 9E: Find a b. 9. | a | = 7, | b | = 4, the angle between a and b is 30
Problem 10E: Find a b. 10. | a | = 80, | b | = 50, the angle between a and b is 3/4
Problem 11E: If u is a unit vector, find u v and u w.
Problem 12E: If u is a unit vector, find u v and u w.
Problem 13E: (a) Show that i j = j k = k i = 0. (b) Show that i i = j j = k k = 1.
Problem 14E: A street vendor sells a hamburgers, b hot dogs, and c soft drinks on a given day. He charges 4 for a...
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E: Find the angle between the vectors. (First find an exact expression and then approximate to the...
Problem 20E: Find the angle between the vectors. (First find an exact expression and then approximate to the...
Problem 21E: Find, correct to the nearest degree, the three angles of the triangle with the given vertices. 21....
Problem 22E: Find, correct to the nearest degree, the three angles of the triangle with the given vertices. 22....
Problem 23E
Problem 24E
Problem 25E: Use vectors to decide whether the triangle with vertices P(l, 3, 2), Q(2, 0, 4), and R{6, 2, 5) is...
Problem 26E: Find the values of x such that the angle between the vectors 2, 1,1, and 1, x, 0 is 45.
Problem 27E: Find a unit vector that is orthogonal to both i + j and i + k.
Problem 28E: Find two unit vectors that make an angle of 60 with v = 3, 4.
Problem 29E: Find the acute angle between the lines. Use degrees rounded to one decimal place. 29. y=43x,y=3x+2
Problem 30E
Problem 31E: Find the acute angles between the curves at their points of intersection. (The angle between two...
Problem 32E: Find the acute angles between the curves at their points of intersection. (The angle between two...
Problem 33E: Find the direction cosines and direction angles of the vector. (Give the direction angles correct to...
Problem 34E: Find the direction cosines and direction angles of the vector. (Give the direction angles correct to...
Problem 35E: Find the direction cosines and direction angles of the vector. (Give the direction angles correct to...
Problem 36E: Find the direction cosines and direction angles of the vector. (Give the direction angles correct to...
Problem 37E: Find the direction cosines and direction angles of the vector. (Give the direction angles correct to...
Problem 38E
Problem 39E: Find the scalar and vector projections of b onto a. 39. a = 5, 12, b = 4, 6
Problem 40E: Find the scalar and vector projections of b onto a. 40. a = 1, 4, b = 2, 3
Problem 41E: Find the scalar and vector projections of b onto a. 41. a = 4, 7, 4, b = 3, 1, 1
Problem 42E: Find the scalar and vector projections of b onto a. 42. a = 1, 4, 8, b = 12, 1, 2
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E: Suppose that a and b are nonzero vectors. (a) Under what circumstances is compa b = compb a? (b)...
Problem 49E
Problem 50E: A tow truck drags a stalled car along a road. The chain makes an angle of 30 with the road and the...
Problem 51E
Problem 52E: A boat sails south with the help of a wind blowing in the direction S36E with magnitude 400 lb. Find...
Problem 53E: Distance from a Point to a Line Use a scalar projection to show that the distance from a point...
Problem 54E: If r = x, y, z a = a1, a2, a3, and b = b1, b2, b3, show that the vector equation (r a) (r b) = 0...
Problem 55E
Problem 56E
Problem 57E
Problem 58E: If c = | a | b + | b | a, where a, b, and c are all nonzero vectors, show that c bisects the angle...
Problem 59E: Prove Properties 2.4, and 5 of the dot product (Theorem 2).
Problem 60E: Suppose that all sides of a quadrilateral are equal in length and opposite sides are parallel. Use...
Problem 61E: Cauchy-Schwartz Inequality Use Theorem 3 to prove the Cauchy-Schwarz Inequality: abab
Problem 62E: Triangle Inequality The Triangle Inequality for vectors is a+ba+b (a) Give a geometric...
Problem 63E: Parallelogram Identity The Parallelogram Identity states that a+b2+ab2=2a2+2b2 (a) Give a geometric...
Problem 64E
Problem 65E
Problem 66E
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