Suppose line L connects points Q and R and suppose point P is not on L. Let point S be the unique point on L such that line PS is perpendicular to L. Then b=QP. Now consider right triangle PQS formed by QP, PS, QS. By the properties of right triangles, sin(8) b) sin(8). d= w Since 8 is the angle between b and a, by the given theorem sin(8) d= [b] sin(0) - b la x bl al b v as was to be shown. Jax bl la) la x b la cos(8) Thus, ) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 9, 6) and R(-1, 3, 6). -d is the maximum distance from point P to line L. Let a QR and
Suppose line L connects points Q and R and suppose point P is not on L. Let point S be the unique point on L such that line PS is perpendicular to L. Then b=QP. Now consider right triangle PQS formed by QP, PS, QS. By the properties of right triangles, sin(8) b) sin(8). d= w Since 8 is the angle between b and a, by the given theorem sin(8) d= [b] sin(0) - b la x bl al b v as was to be shown. Jax bl la) la x b la cos(8) Thus, ) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 9, 6) and R(-1, 3, 6). -d is the maximum distance from point P to line L. Let a QR and
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Transcribed Image Text:Suppose line L connects points Q and R and suppose point P is not on L. Let point S be the unique point on L such that line PS is perpendicular to L. Then PS-d is the maximum distance from point P to line L. Let a = QR and
b = QP.
Now consider right triangle PQS formed by QP, PS, QS. By the properties of right triangles,
d-QP
QP sin(8)= |b) sin(8).
Since is the angle between b and a, by the given theorem sin(8) =
d= |b| sin(0) -
b la x bl
lal bl V
as was to be shown.
Ja x bl
al
la x bl
la cos(8)
Thus,
(b) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 9, 6) and R(-1, 3, 6).
Expert Solution
Step 1
Answer: The solution is given below:
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning