Given the three points A(5, 2, -4), B(7, 4, -2), C(5, 4, 6), let: • S1 be the sphere with centre A and radius 4, • S2 be the sphere which has the line segment BC as a diameter, • T be the circle of intersection of S1 and S2, · E be the centre of T, • L1 be the line through B and E, 2 • L2 be the line through A parallel to 2 1
Given the three points A(5, 2, -4), B(7, 4, -2), C(5, 4, 6), let: • S1 be the sphere with centre A and radius 4, • S2 be the sphere which has the line segment BC as a diameter, • T be the circle of intersection of S1 and S2, · E be the centre of T, • L1 be the line through B and E, 2 • L2 be the line through A parallel to 2 1
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 22CT
Related questions
Question
4
![Given the three points A(5, 2, -4), B(7, 4, -2), C(5, 4, 6), let:
• S1 be the sphere with centre A and radius 4,
• S2 be the sphere which has the line segment BC as a diameter,
• T be the circle of intersection of S1 and S2,
· E be the centre of T,
• L1 be the line through B and E,
2
• L2 be the line through A parallel to
2
Using the geom3d package, or otherwise:
(i) Find the coordinates of E and enter them in the box below. You should enclose the coordinates with square
brackets, eg [1,2,3], and your answer should be exact, ie not a decimal approximation. To prevent typing errors you
can copy and paste the answer from your Maple worksheet.
(ii) Find a decimal approximation to the angle (in radians) between L1 and L2. Your answer should be correct to 10
significant figures. Enter your answer in the box below.
(iii) Find the distance between L1 and L2. Your answer should be exact, not a decimal approximation. Enter your
answer in the box below using Maple syntax. To prevent typing errors you can copy and paste the answer from your
Maple worksheet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdce8f65f-6b59-4ff9-b6c8-f51251924a92%2Fd464ac0b-00f7-4ff5-aaf0-e95073a97881%2Fgsigcu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the three points A(5, 2, -4), B(7, 4, -2), C(5, 4, 6), let:
• S1 be the sphere with centre A and radius 4,
• S2 be the sphere which has the line segment BC as a diameter,
• T be the circle of intersection of S1 and S2,
· E be the centre of T,
• L1 be the line through B and E,
2
• L2 be the line through A parallel to
2
Using the geom3d package, or otherwise:
(i) Find the coordinates of E and enter them in the box below. You should enclose the coordinates with square
brackets, eg [1,2,3], and your answer should be exact, ie not a decimal approximation. To prevent typing errors you
can copy and paste the answer from your Maple worksheet.
(ii) Find a decimal approximation to the angle (in radians) between L1 and L2. Your answer should be correct to 10
significant figures. Enter your answer in the box below.
(iii) Find the distance between L1 and L2. Your answer should be exact, not a decimal approximation. Enter your
answer in the box below using Maple syntax. To prevent typing errors you can copy and paste the answer from your
Maple worksheet.
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