 11.4.1: The _______ vector for a line is parallel to
 11.4.2: The _______ _______ of a line in space are given by and
 11.4.3: When the direction numbers and of the vector are all nonzero, you c...
 11.4.4: A vector that is perpendicular to a plane is called _______ .
 11.4.5: 0, 0, 0 v 1, 2, 3 11
 11.4.6: 3, 5, 1 v 3, 7, 10 0,
 11.4.7: 4, 1, 0 j v 12 i 43 4, 1, 0 j k3,
 11.4.8: 2, 0, 3 v 2i 4j 2k v
 11.4.9: 2, 3, 5 x 5 2t, y 7 3t, z 2 t 2, 0,
 11.4.10: 1, 0, 1 x 3 3t, y 5 2t, z 7 t 2, 3,
 11.4.11: 2, 0, 2, 1, 4, 3 2, 3
 11.4.12: 2, 3, 0, 10, 8, 12 1,
 11.4.13: 3, 8, 15, 1, 2, 16 2, 3
 11.4.14: 2, 3, 1, 1, 5, 3 2,
 11.4.15: 3, 1, 2, 1, 1, 5 2, 1
 11.4.16: 2, 1, 5, 2, 1, 3 3,
 11.4.17: , 2, 1 2, 2, 1 2, 1,1 2, 0 3, 1
 11.4.18: 3, 5, 4 3 2, 3 2 , 2, 1 2
 11.4.19: x 2t, y 2 t, t z 1 12 x 2t, y 2 t, t 3,
 11.4.20: x 5 2t, y 1 t, t z 5 12 x 5 2t, y 1 t, tz
 11.4.21: 2, 1, 2 n i z
 11.4.22: 1, 0, 3 n k 2,
 11.4.23: 5, 6, 3 n 2i j 2k 1, 0
 11.4.24: 0, 0, 0 n 3j 5k 5,
 11.4.25: 2, 0, 0 x 3 t, y 2 2t, z 4 t 0, 0,
 11.4.26: 0, 0, 6 x 1 t, y 2 t, z 4 2t 2, 0,
 11.4.27: 0, 0, 0, 1, 2, 3, 2, 3, 3 0, 0,
 11.4.28: 4, 1, 3, 2, 5, 1, 1, 2, 1 0, 0,
 11.4.29: 2, 3, 2, 3, 4, 2, 1, 1, 0 4, 1,
 11.4.30: 5, 1, 4, 1, 1, 2, 2, 1, 3 2, 3,
 11.4.31: Passes through and is parallel to the plane
 11.4.32: Passes through and is parallel to the plane
 11.4.33: Passes through and and is perpendicular to the plane
 11.4.34: Passes through and and is perpendicular to the plane
 11.4.35: Passes through and and is perpendicular to
 11.4.36: Passes through and and is
 11.4.37: 5x x 3y 4y z 4 7z 1 2x
 11.4.38: 3x 9x y 3y 4z 3 12z 4 5x
 11.4.39: 2x z 1 x 4x y 8z 10 5x
 11.4.40: x 5y z 1 3 5x 25y 5z 32
 11.4.41: Passes through and is parallel to the plane and the plane
 11.4.42: Passes through and is parallel to the plane and the plane
 11.4.43: Passes through and is perpendicular to
 11.4.44: Passes through and is perpendicular to
 11.4.45: Passes through and is parallel to
 11.4.46: Passes through and is parallel to
 11.4.47: x y 2z 0 x 2x y 3z 0 3x
 11.4.48: x 3y 2z 0 v 3x 2y 5z 0x
 11.4.49: 3x 4y 5z 6 x x y z 2 2x
 11.4.50: x 3y z 2 2x 5z 3 0 3
 11.4.51: x y z 0 2 2x 5y z 1
 11.4.52: 2x 4y 2z 1 x 3x 6y 3z 10x
 11.4.53: x 2y 3z 6 2x
 11.4.54: 2x y 4z 4
 11.4.55: x 2y 4 y
 11.4.56: y z 5 x
 11.4.57: 3x 2y z 6 x
 11.4.58: x 3z 6
 11.4.59: 0, 0, 0 3, 8x 4y z 8 x
 11.4.60: 3, 2, 1 3 x y 2z 40
 11.4.61: 1, 3, 4 1, 4x 5y 2z 6 3x
 11.4.62: 1, 4, 7 8x 3x 4y z 91,
 11.4.63: 2, 4, 3 1 2x 3y 2z 4 x
 11.4.64: 1, 3, 6 4 x 2y 2z 32
 11.4.65: 4, 2, 2 1 2x y z 4 2
 11.4.66: 1, 2, 5 2 2x 3y z 124,
 11.4.67: Mechanical Design A chute at the top of a grain elevator of a combi...
 11.4.68: Product Design A bread pan istapered so that aloaf of bread canbe r...
 11.4.69: Two lines in space are either parallel or they intersect.
 11.4.70: Two nonparallel planes in space will always intersect.
 11.4.71: Think About It The direction numbers of two distinct lines in space...
 11.4.72: HOW DO YOU SEE IT? Two planes and their normal vectors are shown be...
Solutions for Chapter 11.4: Lines and Planes in Space
Full solutions for Precalculus with Limits  3rd Edition
ISBN: 9781133947202
Solutions for Chapter 11.4: Lines and Planes in Space
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus with Limits, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.4: Lines and Planes in Space includes 72 full stepbystep solutions. Precalculus with Limits was written by and is associated to the ISBN: 9781133947202. Since 72 problems in chapter 11.4: Lines and Planes in Space have been answered, more than 36011 students have viewed full stepbystep solutions from this chapter.

Absolute value of a vector
See Magnitude of a vector.

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

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

Census
An observational study that gathers data from an entire population

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

Doubleangle identity
An identity involving a trigonometric function of 2u

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Factored form
The left side of u(v + w) = uv + uw.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Negative linear correlation
See Linear correlation.

nth root of unity
A complex number v such that vn = 1

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

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Sum of an infinite series
See Convergence of a series

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

Zoom out
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).