 10.1: (a) Find an equation of the sphere that passes through the point an...
 10.2: Copy the vectors in the figure and use them to draw each of the fol...
 10.3: If u and v are the vectors shown in the figure, find and . Is u v d...
 10.4: Calculate the given quantity if The angle between and (correct to t...
 10.5: Find the values of such that the vectors and are orthogonal.
 10.6: Find two unit vectors that are orthogonal to both and
 10.7: Suppose that . Find
 10.8: Show that if , , and are in , then
 10.9: Find the acute angle between two diagonals of a cube.
 10.10: Given the points , , , and , find the volume of the parallelepiped ...
 10.11: (a) Find a vector perpendicular to the plane through the points , ,...
 10.12: A constant force moves an object along the line segment from to . F...
 10.13: A boat is pulled onto shore using two ropes, as shown in the diagra...
 10.14: Find the magnitude of the torque about if a 50N force is applied a...
 10.15: Find parametric equations for the line. The line through and
 10.16: Find parametric equations for the line The line through and paralle...
 10.17: Find parametric equations for the line The line through and perpend...
 10.18: Find an equation of the plane.The plane through and parallel to
 10.19: Find an equation of the plane.The plane through , , and
 10.20: Find an equation of the plane.The plane through that contains the line
 10.21: Find the point in which the line with parametric equations , , inte...
 10.22: Find the distance from the origin to the line
 10.23: Determine whether the lines given by the symmetric equations and ar...
 10.24: (a) Show that the planes and are neither parallel nor perpendicular...
 10.25: Find an equation of the plane through the line of intersection of t...
 10.26: (a) Find an equation of the plane that passes through the points , ...
 10.27: Find the distance between the planes and .
 10.28: Identify and sketch the graph of each surface.
 10.29: Identify and sketch the graph of each surface.
 10.30: Identify and sketch the graph of each surface.
 10.31: Identify and sketch the graph of each surface.
 10.32: Identify and sketch the graph of each surface.
 10.33: Identify and sketch the graph of each surface.
 10.34: Identify and sketch the graph of each surface.
 10.35: Identify and sketch the graph of each surface.
 10.36: Identify and sketch the graph of each surface.
 10.37: An ellipsoid is created by rotating the ellipse about the axis. Fi...
 10.38: A surface consists of all points such that the distance from to the...
 10.39: (a) Sketch the curve with vector function (b) Find and
 10.40: Let . (a) Find the domain of . (b) Find . (c) Find
 10.41: Find a vector function that represents the curve of intersection of...
 10.42: Find parametric equations for the tangent line to the curve , , at ...
 10.43: If , evaluate
 10.44: Let be the curve with equations , , . Find (a) the point where inte...
 10.45: Use Simpsons Rule with to estimate the length of the arc of the cur...
 10.46: Find the length of the curve
 10.47: The helix intersects the curve at the point . Find the angle of int...
 10.48: Reparametrize the curve with respect to arc length measured from th...
 10.49: For the curve given by , find (a) the unit tangent vector, (b) the ...
 10.50: Find the curvature of the ellipse , at the points and
 10.51: Find the curvature of the curve at the point
 10.52: Find an equation of the osculating circle of the curve at the origi...
 10.53: A particle moves with position function Find the velocity, speed, a...
 10.54: A particle starts at the origin with initial velocity . Its acceler...
 10.55: An athlete throws a shot at an angle of to the horizontal at an ini...
 10.56: Find the tangential and normal components of the acceleration vecto...
 10.57: Find the curvature of the curve with parametric equations
Solutions for Chapter 10: Vectors and the Geometry of Space
Full solutions for Essential Calculus  2nd Edition
ISBN: 9781133112297
Solutions for Chapter 10: Vectors and the Geometry of Space
Get Full SolutionsSummary of Chapter 10: Vectors and the Geometry of Space
In this chapter we will see that vectors provide particularly simple descriptions of lines, planes, and curves. We will also use vectorvalued functions to describe the motion of objects through space. In particular, we will use them to derive Kepler’s laws of planetary motion.
Essential Calculus was written by and is associated to the ISBN: 9781133112297. Chapter 10: Vectors and the Geometry of Space includes 57 full stepbystep solutions. This textbook survival guide was created for the textbook: Essential Calculus, edition: 2. Since 57 problems in chapter 10: Vectors and the Geometry of Space have been answered, more than 26592 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Anchor
See Mathematical induction.

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

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

Convenience sample
A sample that sacrifices randomness for convenience

Divisor of a polynomial
See Division algorithm for polynomials.

Explanatory variable
A variable that affects a response variable.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Imaginary axis
See Complex plane.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Length of an arrow
See Magnitude of an arrow.

Linear regression equation
Equation of a linear regression line

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

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

Positive angle
Angle generated by a counterclockwise rotation.

Root of a number
See Principal nth root.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Zero factor property
If ab = 0 , then either a = 0 or b = 0.