In nature, substances often possess a crystalline structure. The basic component of a crystal is the unit cell, such as the rectangular parallelepiped shown. ( Figure 1) (For this problem, take L₁, L2, and L3 as positive.) When a question asks for a vector, express your answer as an ordered triplet. That is, a vector with Figure A H O L₁ V₂ V3 S B G 1 of 1 2.6.4 Part C What is V3. the vector from point O to point C? Express your answer in terms of some or all the variables L₁, L2, and L3. V₂ = Part D VAΣo↓t vec 1 What is the sum 2V3 + 3V₂? Express your answer in terms of some or all the variables L₁, L2, and L3. ▸ View Available Hint(s) 195] ΑΣΦ 2V3+ 3V2= Part E V₂ = Ivec IT vec ? 1 What is the length of vector V₁? Express your answer in terms of some or all the variables L₁, L2, and L3. ▸ View Available Hint(s) IVE| ΑΣΦ WWW ? ?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 14EQ: In Figure 1.24, A, B, C, D, E, and F are the vertices of a regular hexagon centered at the origin....
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In nature, substances often possess a crystalline
structure. The basic component of a crystal is the unit
cell, such as the rectangular parallelepiped shown. (
Figure 1) (For this problem, take L₁, L2, and L3 as
positive.)
When a question asks for a vector, express your
answer as an ordered triplet. That is, a vector with
Figure
L3
E
A
H
L₁
V₂
V3
S
B
G
C
1 of 1
2.6.4
:0
Part C
What is V3. the vector from point O to point C?
Express your answer in terms of some or all the variables L₁, L2, and L3.
V3 =
Part D
V—| ΑΣΦ
2V3+ 3V2 =
Part E
What is the sum 2V3 + 3V2?
Express your answer in terms of some or all the variables L₁, L2, and L3-
▸ View Available Hint(s)
VE ΑΣΦ ↓↑ vec
V₁ =
↓↑vec
[5] ΑΣΦ
?
What is the length of vector V₁?
Express your answer in terms of some or all the variables L₁, L2, and L3.
► View Available Hint(s)
↓↑ vec
?
?
Transcribed Image Text:In nature, substances often possess a crystalline structure. The basic component of a crystal is the unit cell, such as the rectangular parallelepiped shown. ( Figure 1) (For this problem, take L₁, L2, and L3 as positive.) When a question asks for a vector, express your answer as an ordered triplet. That is, a vector with Figure L3 E A H L₁ V₂ V3 S B G C 1 of 1 2.6.4 :0 Part C What is V3. the vector from point O to point C? Express your answer in terms of some or all the variables L₁, L2, and L3. V3 = Part D V—| ΑΣΦ 2V3+ 3V2 = Part E What is the sum 2V3 + 3V2? Express your answer in terms of some or all the variables L₁, L2, and L3- ▸ View Available Hint(s) VE ΑΣΦ ↓↑ vec V₁ = ↓↑vec [5] ΑΣΦ ? What is the length of vector V₁? Express your answer in terms of some or all the variables L₁, L2, and L3. ► View Available Hint(s) ↓↑ vec ? ?
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