Maple1231W7T5 - 3D Geometry

Friday, 7 September 2018

6:57 PM

Untitled picture.png Machine generated alternative text:
Use Maple to find the cross product of 
vector(3, = 432296259' 
Use Maple to find the dot product of 
-364256512243 
Use Maple to find the dot product of 
1788274354354 
-809735 
-986145 
-400152 
-809735 
-986145 
-400152 
-809735 
-986145 
-400152 
and 
and 
and 
316163 
246982 
-338151 
316163 
246982 
-338151 
-809735 
-986145 
-400152 
-809735 
-986145 
-400152 
and enter your answer in the box below (You should use Maple's angle bracket notation for vectors.) 
and enter your answer in the box below. 
and enter your answer in the box below. 
and enter your answer in the box below. 
Use the Maple command Norm to find the exact length of 
sqä(1788274354354) 
Note: To avoid typos, you may copy the following to your Maple worksheet and copy the answers from your Maple worksheets to the above answer boxes. 
-809735, 
-986145, -4€€152 
316163, 246982, -338151 
Maple treats 0.5 as an approximation while 1/2 as exact 

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:
-400152) : 
b: (3161632246982: -338151): 
with (Linear-4 lgebra) 
CrossProduct( b) 
432296259159 
-400325956761 
111792591865 
-364256512243 
Norm (4 2) 
1788274354354 
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 
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
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 
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
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 
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

 

Created with Microsoft OneNote 2016.