 11.2.1: The _______ vector is denoted by
 11.2.2: The standard unit vector notation for a vector is _______ .
 11.2.3: The _______ _______ of a vector is produced by subtracting the coor...
 11.2.4: If the dot product of two nonzero vectors is zero, then the angle b...
 11.2.5: Two nonzero vectors and are _______ when there is some scalar such ...
 11.2.6: The points and are _______ if and only if the vectors and are paral...
 11.2.7: 5 3 z (5, 3, 1) (5, 3, 1)
 11.2.8: (1, 4, 4) (1, 4, 0)
 11.2.9: (2, 0, 1) (0, 3, 2)
 11.2.10: (1, 2, 4) (0, 4, 4)
 11.2.11: 6, 4, 2 1, 1, 3
 11.2.12: 7, 3, 5 0, 0, 2
 11.2.13: 1, 2, 4 1, 4, 4
 11.2.14: 0, 1, 0 0, 2, 1
 11.2.15: v 1, 1, 3 0 (a) (b) (c) (d)
 11.2.16: v 1, 2, 2 0v (a) (b) (c) (d)
 11.2.17: v 2i 2j k (a) (b) (c) (d)
 11.2.18: v i 2j k (a) (b) (c) (d)
 11.2.19: z u 2v 5
 11.2.20: z 7u v 1 z u 2v 5w w
 11.2.21: 2z 4u w u
 11.2.22: u v z 0
 11.2.23: z 2u 3v 1 2w 2
 11.2.24: z 3w 2v u
 11.2.25: v 7, 8, 7 v
 11.2.26: v 2, 0, 5 z
 11.2.27: v 1, 2, 4 v
 11.2.28: v 1, 0, 3 v
 11.2.29: v i 3j k v
 11.2.30: v i 4j 3k
 11.2.31: v 4i 3j 7k v
 11.2.32: v 2i j 6k
 11.2.33: Initial point: terminal point:
 11.2.34: Initial point: terminal point:
 11.2.35: u 8i 3j k u
 11.2.36: u 3i 5j 10k
 11.2.37: u 4, 4, 1 u v 2, 5, 8 v
 11.2.38: u 3, 1, 6 u v 4, 10, 1u
 11.2.39: u 2i 5j 3k u v 9i 3j k v
 11.2.40: u 3j 6kv 6i 4j 2k
 11.2.41: u 0, 2, 2 u v 3, 0, 4 v
 11.2.42: u 1, 3, 0 v 1, 2, 1u
 11.2.43: u 10i 40j u v 3j 8k v
 11.2.44: u 8j 20k v 10i 5k
 11.2.45: u 12, 6, 15 u v 8, 4, 10 v
 11.2.46: u 1, 3, 1 Th v 2, 1, 5u
 11.2.47: u 0, 1, 6 u v 1, 2, 1 v
 11.2.48: u 0, 4, 1 v v 1, 0, 0u
 11.2.49: u j k 3 4 i 1 2 j 2k v 4i 10j k v
 11.2.50: u i 1 2 u j k 3 v 8i 4j 8k
 11.2.51: u 2i 3j k u v 2i j k v
 11.2.52: u 2i 3j k v i j k
 11.2.53: 5, 4, 1, 7, 3, 1, 4, 5, 3
 11.2.54: 2, 7, 4, 4, 8, 1, 0, 6, 7
 11.2.55: 1, 3, 2, 1, 2, 5, 3, 4, 1
 11.2.56: 0, 4, 4, 1, 5, 6, 2, 6, 7
 11.2.57: v 2, 4, 7 v
 11.2.58: v 4, 1, 1 0
 11.2.59: v 4, , 4 3 2, 1 4 1
 11.2.60: v 5 2, 1 2 v 4, , 4 3 2,
 11.2.61: cu 3, u i 2j 3k c
 11.2.62: cu 12, u 2i 2j 4k
 11.2.63: Vector lies in the plane, has magnitude 4, and makes an angle of w...
 11.2.64: Vector lies in the plane, has magnitude 10, and makes an angle of ...
 11.2.65: Tension The weight of a crate is 500 newtons. Find the tension in e...
 11.2.66: Tension The lights in an auditorium are 24pound disks of radius18 ...
 11.2.67: If the dot product of two nonzero vectors is zero, then the angle b...
 11.2.68: If and are parallel vectors, then points and are collinear.
 11.2.69: Think About It What is known about the nonzero vectors and when Exp...
 11.2.70: HOW DO YOU SEE IT? Use the figure below. (a) Find and (b) A vector ...
Solutions for Chapter 11.2: Vectors in Space
Full solutions for Precalculus with Limits  3rd Edition
ISBN: 9781133947202
Solutions for Chapter 11.2: Vectors in Space
Get Full SolutionsPrecalculus with Limits was written by and is associated to the ISBN: 9781133947202. Since 70 problems in chapter 11.2: Vectors in Space have been answered, more than 35898 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.2: Vectors in Space includes 70 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus with Limits, edition: 3.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Addition property of equality
If u = v and w = z , then u + w = v + z

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Cotangent
The function y = cot x

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

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

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

Irrational zeros
Zeros of a function that are irrational numbers.

Length of a vector
See Magnitude of a vector.

Minute
Angle measure equal to 1/60 of a degree.

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Range screen
See Viewing window.

Real number line
A horizontal line that represents the set of real numbers.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Wrapping function
The function that associates points on the unit circle with points on the real number line

Xmin
The xvalue of the left side of the viewing window,.

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.