Consider the line li joining the points A(-5,-3,0) and B(7,1,4). 1. Find the parametric equation of the line. 2. Show that the point C(1,-1,2) lies on the line. 3. Show that the point D(-4,3,2) is not on the line.
Consider the line li joining the points A(-5,-3,0) and B(7,1,4). 1. Find the parametric equation of the line. 2. Show that the point C(1,-1,2) lies on the line. 3. Show that the point D(-4,3,2) is not on the line.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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Question
![ul MTN ,
11:44 PM
@ 46%
You
All Media
17/02/2021, 7:16 PM
Department of Mathematics
University of Ghana
Math123: Vectors and Geometry
Module 4: Exercise 3
Module 4 (Lines in Space)
TK/GAB/JB/EKAS/KD/JDGM
15/02/2021
Consider the line li joining the points A(-5,-3,0) and B(7, 1,4).
1. Find the parametric equation of the line.
2. Show that the point C(1, -1, 2) lies on the line.
3. Show that the point D(-4, 3, 2) is not on the line.
4. Find the foot of the perpendicular Q from D to the line and determine the shortest
distance between the point and the line.
5. The line l, intersects the line la given by r 12i-3j + 4k + 4(-8i + 3j -k).
(a) Find the position vector of the point Rof intersection.
(b) Find the angle between the two lines.
(c) Find the equations of the internal and extemal bisectors of the angle between the
lines and l2.
(d) The point D is on l. Find a point D' such that DO = QD.
(c) Find the equation of the line joining R and D'.
(f) Show that l4 is the bisector of angle DRD. Line is the mirror image of the line
lz in 1]
Figure 1:
Is it this please](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F706d29d0-3759-496d-9920-c95d0acef5c0%2Ff7f534ac-2cb7-48e5-9abc-b4ddc86bd516%2Fcaapygi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ul MTN ,
11:44 PM
@ 46%
You
All Media
17/02/2021, 7:16 PM
Department of Mathematics
University of Ghana
Math123: Vectors and Geometry
Module 4: Exercise 3
Module 4 (Lines in Space)
TK/GAB/JB/EKAS/KD/JDGM
15/02/2021
Consider the line li joining the points A(-5,-3,0) and B(7, 1,4).
1. Find the parametric equation of the line.
2. Show that the point C(1, -1, 2) lies on the line.
3. Show that the point D(-4, 3, 2) is not on the line.
4. Find the foot of the perpendicular Q from D to the line and determine the shortest
distance between the point and the line.
5. The line l, intersects the line la given by r 12i-3j + 4k + 4(-8i + 3j -k).
(a) Find the position vector of the point Rof intersection.
(b) Find the angle between the two lines.
(c) Find the equations of the internal and extemal bisectors of the angle between the
lines and l2.
(d) The point D is on l. Find a point D' such that DO = QD.
(c) Find the equation of the line joining R and D'.
(f) Show that l4 is the bisector of angle DRD. Line is the mirror image of the line
lz in 1]
Figure 1:
Is it this please
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