 9.4.1: Let x = [1, 4,1]_ and y = [2, 1, 0]_. (a) Find x + y. (b) Find 2x. ...
 9.4.2: Let x = [4, 3, 1]_ and y = [0,2, 3]_. (a) Find x y. (b) Find 2x + 3...
 9.4.3: Let A = (2, 3) and B = (4, 1). Find the vector representation of AB.
 9.4.4: Let A = (1, 0) and B = (2,4). Find the vector representation of AB.
 9.4.5: Let A = (0, 1,3) and B = (1,1, 2). Find the vector representation o...
 9.4.6: Let A = (1, 3,2) and B = (0,1, 0). Find the vector representation o...
 9.4.7: Find the length of x = [1, 3]_.
 9.4.8: Find the length of x = [2, 7]_.
 9.4.9: Find the length of x = [0, 1, 5]_.
 9.4.10: Find the length of x = [2, 1,3]_.
 9.4.11: Normalize [1, 3,1]_.
 9.4.12: Normalize [2, 0,4]_.
 9.4.13: Normalize [6, 0, 0]_.
 9.4.14: Normalize [0,3, 1, 3]_.
 9.4.15: Find the dot product of x = [1, 2]_ and y = [3,1]_.
 9.4.16: Find the dot product of x = [1, 2]_ and y = [3,4]_.
 9.4.17: Find the dot product of x = [0,1, 3]_ and y = [3, 1, 1]_.
 9.4.18: Find the dot product of x = [2,3, 1]_ and y = [3, 1,2]_.
 9.4.19: Use the dot product to compute the length of [0,1, 2]_.
 9.4.20: Use the dot product to compute the length of [1, 4, 3]_.
 9.4.21: Use the dot product to compute the length of [1, 2, 3, 4]_.
 9.4.22: Use the dot product to compute the length of [1,2,3,4]_.
 9.4.23: Find the angle between x = [1, 2]_ and y = [3,1]_.
 9.4.24: Find the angle between x = [1, 2]_ and y = [2,4]_.
 9.4.25: Find the angle between x = [0,1, 3]_ and y = [3, 1, 1]_.
 9.4.26: Find the angle between x = [1,3, 2]_ and y = [3, 1,4]_.
 9.4.27: Let x = [1,1]_. Find y so that x and y are perpendicular.
 9.4.28: Let x = [2, 1]_. Find y so that x and y are perpendicular.
 9.4.29: Let x = [1,2, 4]_. Find y so that x and y are perpendicular.
 9.4.30: Let x = [2, 0,1]_. Find y so that x and y are perpendicular.
 9.4.31: A triangle has vertices at coordinates P = (0, 0), Q = (4, 0), and ...
 9.4.32: A triangle has vertices at coordinates P = (0, 0), Q = (0, 3), and ...
 9.4.33: A triangle has vertices at coordinates P = (1, 2, 3), Q = (1, 5, 2)...
 9.4.34: A triangle has vertices at coordinates P = (2, 1, 5), Q = (1,3, 7),...
 9.4.35: Find the equation of the line through (2, 1) and perpendicular to [...
 9.4.36: Find the equation of the line through (3, 2) and perpendicular to [...
 9.4.37: Find the equation of the line through (1,2) and perpendicular to [4...
 9.4.38: Find the equation of the line through (0, 1) and perpendicular to [...
 9.4.39: Find the equation of the plane through (1, 2, 3) and perpendicular ...
 9.4.40: Find the equation of the plane through (1, 0,3) and perpendicular t...
 9.4.41: Find the equation of the plane through (0, 0, 0) and perpendicular ...
 9.4.42: Find the equation of the plane through (3,1, 2) and perpendicular t...
 9.4.43: In 4346, find the parametric equation of the line in the xy plane t...
 9.4.44: In 4346, find the parametric equation of the line in the xy plane t...
 9.4.45: In 4346, find the parametric equation of the line in the xy plane t...
 9.4.46: In 4346, find the parametric equation of the line in the xy plane t...
 9.4.47: In 4750, find the parametric equation of the line in the xy plane t...
 9.4.48: In 4750, find the parametric equation of the line in the xy plane t...
 9.4.49: In 4750, find the parametric equation of the line in the xy plane t...
 9.4.50: In 4750, find the parametric equation of the line in the xy plane t...
 9.4.51: In 5154, parameterize the equation of the line given in standard fo...
 9.4.52: In 5154, parameterize the equation of the line given in standard fo...
 9.4.53: In 5154, parameterize the equation of the line given in standard fo...
 9.4.54: In 5154, parameterize the equation of the line given in standard fo...
 9.4.55: In 5558, find the parametric equation of the line in x yz space tha...
 9.4.56: In 5558, find the parametric equation of the line in x yz space tha...
 9.4.57: In 5558, find the parametric equation of the line in x yz space tha...
 9.4.58: In 5558, find the parametric equation of the line in x yz space tha...
 9.4.59: In 5962, find the parametric equation of the line in x yz space tha...
 9.4.60: In 5962, find the parametric equation of the line in x yz space tha...
 9.4.61: In 5962, find the parametric equation of the line in x yz space tha...
 9.4.62: In 5962, find the parametric equation of the line in x yz space tha...
 9.4.63: Given are (1) a plane through (1, 1, 2) and perpendicular to 1 2 1 ...
 9.4.64: Given are (1) a plane through (2, 0,1) and perpendicular to 1 1 3 a...
 9.4.65: Given is a plane through (0,2, 1) and perpendicular to 1 1 1 . Find...
 9.4.66: Given is the plane x+2yz+1 = 0. Find a line in parametric form that...
Solutions for Chapter 9.4: Analytic Geometry
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 9.4: Analytic Geometry
Get Full SolutionsChapter 9.4: Analytic Geometry includes 66 full stepbystep solutions. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by and is associated to the ISBN: 9780321644688. Since 66 problems in chapter 9.4: Analytic Geometry have been answered, more than 21461 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus For Biology and Medicine (Calculus for Life Sciences Series), edition: 3. This expansive textbook survival guide covers the following chapters and their solutions.

Additive identity for the complex numbers
0 + 0i is the complex number zero

Anchor
See Mathematical induction.

Arccosecant function
See Inverse cosecant function.

Arccotangent function
See Inverse cotangent function.

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

Exponent
See nth power of a.

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Focal length of a parabola
The directed distance from the vertex to the focus.

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

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

Intercepted arc
Arc of a circle between the initial side and terminal side of a central angle.

Inverse function
The inverse relation of a onetoone function.

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Parametrization
A set of parametric equations for a curve.

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.