 11.1: (a) What is the difference between a vector and a scalar?Give a phy...
 11.2: (a) Sketch vectors u and v for which u + v and u v areorthogonal.(b...
 11.3: (a) Draw a picture that shows the direction angles , , and of a vec...
 11.4: (a) Make a table that shows all possible cross products ofthe vecto...
 11.5: In each part, find an equation of the sphere with center(3, 5, 4) a...
 11.6: Find the largest and smallest distances between the pointP (1, 1, 1...
 11.7: Given the points P (3, 4), Q(1, 1), and R(5, 2), use vectormethods ...
 11.8: Let u = 3, 5, 1 and v = 2, 2, 3. Find(a) 2u + 5v (b)1vv(c) u (d) u v.
 11.9: Let a = ci + j and b = 4i + 3j. Find c so that(a) a and b are ortho...
 11.10: Let r0 = x0, y0, z0 and r = x, y,z. Describe the set ofall points (...
 11.11: Show that if u and v are unit vectors and is the anglebetween them,...
 11.12: Find the vector with length 5 and direction angles = 60 , = 120 , =...
 11.13: Assuming that force is in pounds and distance is in feet, findthe w...
 11.14: Assuming that force is in newtons and distance is in meters,find th...
 11.15: (a) Find the area of the triangle with vertices A(1, 0, 1),B(0, 2, ...
 11.16: True or false? Explain your reasoning.(a) If u v = 0, then u = 0 or...
 11.17: Consider the pointsA(1, 1, 2), B(2, 3, 0), C(1, 2, 0), D(2, 1, 1)(a...
 11.18: Suppose that a force F with a magnitude of 9 lb is applied tothe le...
 11.19: Let P be the point (4, 1, 2). Find parametric equations forthe line...
 11.20: (a) Find parametric equations for the intersection of theplanes 2x ...
 11.21: Find an equation of the plane that is parallel to the planex + 5y z...
 11.22: Find an equation of the plane through the point (4, 3, 0) andparall...
 11.23: What condition must the constants satisfy for the planesa1x + b1y +...
 11.24: (a) List six common types of quadric surfaces, and describetheir tr...
 11.25: In each part, identify the surface by completing the squares.(a) x2...
 11.26: In each part, express the equation in cylindrical and sphericalcoor...
 11.27: In each part, express the equation in rectangular coordinates.(a) z...
 11.28: 2829 Sketch the solid in 3space that is described in cylindricalco...
 11.29: 2829 Sketch the solid in 3space that is described in cylindricalco...
 11.30: 3031 Sketch the solid in 3space that is described in sphericalcoor...
 11.31: 3031 Sketch the solid in 3space that is described in sphericalcoor...
 11.32: Sketch the surface whose equation in spherical coordinatesis = a(1 ...
Solutions for Chapter 11: THREEDIMENSIONAL SPACE; VECTORS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 11: THREEDIMENSIONAL SPACE; VECTORS
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 32 problems in chapter 11: THREEDIMENSIONAL SPACE; VECTORS have been answered, more than 38031 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Chapter 11: THREEDIMENSIONAL SPACE; VECTORS includes 32 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Central angle
An angle whose vertex is the center of a circle

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Dependent variable
Variable representing the range value of a function (usually y)

Direct variation
See Power function.

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

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

Initial side of an angle
See Angle.

Irrational zeros
Zeros of a function that are irrational numbers.

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Obtuse triangle
A triangle in which one angle is greater than 90°.

Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Solve by elimination or substitution
Methods for solving systems of linear equations.

Ymin
The yvalue of the bottom of the viewing window.

Zero matrix
A matrix consisting entirely of zeros.