Maple1231W7T5 - 3D Geometry
Friday, 7 September 2018
6:57 PM
Created with Microsoft OneNote 2016.
![Untitled picture.png Machine generated alternative text:
Which of the following is a correct Maple command that will define the line L; for use with the geom3d package, to be the line passing through the two points A and B? You may assume that the
geom3d package has already been loaded and the pants A and B have already been defined.
0
0
0
0
O
O
O
O
line(L) A, a;
line(L, [A,
A, a line(L);
L line(A, 8);
line(A,
line(IA,
line(L)
line(L);
Untitled picture.png Machine generated alternative text:
Given the three points ,-2), and C(-7 let Ll be the line through A and B and let L 2 be the line through C parallel to (1
the exact value of the distance in the box below
This question accepts formulas in Maple syntax.
Plot I Help Preview
Find the distance beftveen Ll and 12
Exact
Untitled picture.png Machine generated alternative text:
Given the three points A(-2, 2; 2); B(-l, 3; 3), C(6, 6, 7), let:
• Sl 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 Sl and S2,
• E be the centre of T,
• Ll be the line through B and E,
• L2 be the line through A parallel to
Using the geom3d package, or othenvise:
3
2
2
(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
[13/142, 449/142, 241/71]
(ii) Find a decimal approximation to the angle (in radians) between Ll and L 2
0.4322296962
Your answer should be correct to 10 significant figures
Enter your answer in the box below.
(iii) Find the distance between Ll and L 2. Your answer should be exact, not a decimal approximation.
can copy and paste the answer from your Maple worksheet
(3382601 rsqrt(82601)
Enter your answer in the box below using Maple syntax. To prevent typing errors you
Untitled picture.png Machine generated alternative text:
vith( geom 34)
Mint(A, •
71)
sphere(S1. [A, 41)
sphere(S2, [B, C]) •
intersection( T, SIZ S2)
detail( T)
13 449
line(L1, 1B, El)
ltne(L2, [A: [3,
L2), 10)
distance(L1, L2)
name ofthe object
form of the object
of the center
circle3d
center T_l
13 449
coordinates of the center
142 : 142'
radius offfe center
13
142
the circle lies on the plane p
uzne of the object p
241
form o f the obj ect plane3d
71
equationoftheplane —37 + 9 _x+ 5 _v+
0.4322296962
33
82601
S2601
Untitled picture.png Machine generated alternative text:
with(geom3
point(Az
point(C, [ —7.5, —71) _
line(Ll. [A, B l)
åstance(L1, L 2)
1609
v 1361](Maple1231W7T5%20-%203D%20Geometry_files/image003.png)
![Untitled picture.png Machine generated alternative text:
vith( geom 34)
Mint(A, •
71)
sphere(S1. [A, 41)
sphere(S2, [B, C]) •
intersection( T, SIZ S2)
detail( T)
13 449
line(L1, 1B, El)
ltne(L2, [A: [3,
L2), 10)
distance(L1, L2)
name ofthe object
form of the object
of the center
circle3d
center T_l
13 449
coordinates of the center
142 : 142'
radius offfe center
13
142
the circle lies on the plane p
uzne of the object p
241
form o f the obj ect plane3d
71
equationoftheplane —37 + 9 _x+ 5 _v+
0.4322296962
33
82601
S2601
Untitled picture.png Machine generated alternative text:
with(geom3
point(Az
point(C, [ —7.5, —71) _
line(Ll. [A, B l)
åstance(L1, L 2)
1609
v 1361](Maple1231W7T5%20-%203D%20Geometry_files/image004.png)
![Untitled picture.png Machine generated alternative text:
Given the three points A(-2, 2; 2); B(-l, 3; 3), C(6, 6, 7), let:
• Sl 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 Sl and S2,
• E be the centre of T,
• Ll be the line through B and E,
• L2 be the line through A parallel to
Using the geom3d package, or othenvise:
3
2
2
(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
[13/142, 449/142, 241/71]
(ii) Find a decimal approximation to the angle (in radians) between Ll and L 2
0.4322296962
Your answer should be correct to 10 significant figures
Enter your answer in the box below.
(iii) Find the distance between Ll and L 2. Your answer should be exact, not a decimal approximation.
can copy and paste the answer from your Maple worksheet
(3382601 rsqrt(82601)
Enter your answer in the box below using Maple syntax. To prevent typing errors you
Untitled picture.png Machine generated alternative text:
Given the three points A (2, 4, —4), B (5, 5,
2
• L 1 be the line through A parallel to -5
-1
• P be the plane through B with normal 2
-3
• E be the point of intersection of Ll and R
• S be the sphere through A, B, C, E,
• F be the centre of S,
• L 2 be the line through C and E
Using the geom3d package, or othenvise:
(i) Find a decimal approximation to the angle between Ll and R correct to 10 significant figures. Enter your answer in the box below To prevent typing errors you can copy and paste the
answer from your Maple worksheet
-.3623352016
(ii) Find the coordinates of F and enter them in the box below. You should enclose the coordinates with square brackets, eg [1 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
[15/4, 359/56, -103/56]
(iii) Find the distance between A and 12 Your answer should be exact, not a decimal approximation.
copy and paste the answer from your Maple worksheet
Enter your answer in the box below using Maple syntax. To prevent typing errors you can
Untitled picture.png Machine generated alternative text:
vith( geom 34)
Mint(A, •
71)
sphere(S1. [A, 41)
sphere(S2, [B, C]) •
intersection( T, SIZ S2)
detail( T)
13 449
line(L1, 1B, El)
ltne(L2, [A: [3,
L2), 10)
distance(L1, L2)
name ofthe object
form of the object
of the center
circle3d
center T_l
13 449
coordinates of the center
142 : 142'
radius offfe center
13
142
the circle lies on the plane p
uzne of the object p
241
form o f the obj ect plane3d
71
equationoftheplane —37 + 9 _x+ 5 _v+
0.4322296962
33
82601
S2601
Untitled picture.png Machine generated alternative text:
nth(gæm3d)
(2, 4-41)
15, *-51)
nint(c, (3.3,-31) .
[A, [2-5.-111)
[B. [0, 2.-311)
intersection(E_ L l, P) •
sphere(S [A, B, c. E]) •
int(F: ) )
me(L2 [C, F])
istance(A, L2)
-0.3623352016
42470
15
4
359
56
103
56](Maple1231W7T5%20-%203D%20Geometry_files/image005.png)
![Untitled picture.png Machine generated alternative text:
vith( geom 34)
Mint(A, •
71)
sphere(S1. [A, 41)
sphere(S2, [B, C]) •
intersection( T, SIZ S2)
detail( T)
13 449
line(L1, 1B, El)
ltne(L2, [A: [3,
L2), 10)
distance(L1, L2)
name ofthe object
form of the object
of the center
circle3d
center T_l
13 449
coordinates of the center
142 : 142'
radius offfe center
13
142
the circle lies on the plane p
uzne of the object p
241
form o f the obj ect plane3d
71
equationoftheplane —37 + 9 _x+ 5 _v+
0.4322296962
33
82601
S2601
Untitled picture.png Machine generated alternative text:
nth(gæm3d)
(2, 4-41)
15, *-51)
nint(c, (3.3,-31) .
[A, [2-5.-111)
[B. [0, 2.-311)
intersection(E_ L l, P) •
sphere(S [A, B, c. E]) •
int(F: ) )
me(L2 [C, F])
istance(A, L2)
-0.3623352016
42470
15
4
359
56
103
56](Maple1231W7T5%20-%203D%20Geometry_files/image006.png)