Consider the vectors shown in the figure. 4 a3 3 2 a2 a1 |-1 -2 -3 |-4 -4 -3 -2 -1 1 2 3 4 - Part 1: Basic properties The figure shows vectors in R" for n = . The coordinate representation of the zero vector is 0 (use coordinate vector notation, not ijk-vector notation). Part 2: Parallel or not? Are any two of these vectors parallel to each other? - Is ãi parallel to a2? choose - Is ai parallel to az? choose · Is az parallel to a3? choose - Part 3: Coordinate representations

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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Consider the vectors shown in the figure.
4
аз
3
2
a2
a1
|-1
-2
|-3
-4
-4 -3 -2 -1
1 2 3 4
- Part 1: Basic properties
The figure shows
vectors in
R" for n =
The
coordinate representation of the zero
vector is 0
(use
coordinate vector notation, not ijk-vector
notation).
• Part 2: Parallel or not?
Are any two of these vectors parallel to
each other?
- Is ai parallel to a2?
choose
- Is ai parallel to a3?
choose
- Is a2 parallel to a3?
choose
• Part 3: Coordinate representations
Transcribed Image Text:Consider the vectors shown in the figure. 4 аз 3 2 a2 a1 |-1 -2 |-3 -4 -4 -3 -2 -1 1 2 3 4 - Part 1: Basic properties The figure shows vectors in R" for n = The coordinate representation of the zero vector is 0 (use coordinate vector notation, not ijk-vector notation). • Part 2: Parallel or not? Are any two of these vectors parallel to each other? - Is ai parallel to a2? choose - Is ai parallel to a3? choose - Is a2 parallel to a3? choose • Part 3: Coordinate representations
Part 3: Coordinate representations
Find the coordinate representations of
each vector:
1 A2 =
• a3
- Part 4: Finding relationships among these
vectors
Write each of the vectors in terms of the
other vectors. Use the names of vectors in
your answer (e.g., enter 4a2 - 5a3 for
4a2 – 5a3). Do not enter coordinate
representations such as (3, 4).
1 aj =
- āz
1 ɑɔ =
Part 5: Can we combine these vectors to
get the zero vector?
If possible, scale and add the vectors ā1,
a2, and az to obtain the zero vector 0. If
this is not possible, enter DNE.
Use the names of vectors in your answer
(e.g., enter 4a1 - 5a2 + a3 for
4a1 – 5a2 + a3). Do not enter coordinate
representations such as (3, 4).
= .
Transcribed Image Text:Part 3: Coordinate representations Find the coordinate representations of each vector: 1 A2 = • a3 - Part 4: Finding relationships among these vectors Write each of the vectors in terms of the other vectors. Use the names of vectors in your answer (e.g., enter 4a2 - 5a3 for 4a2 – 5a3). Do not enter coordinate representations such as (3, 4). 1 aj = - āz 1 ɑɔ = Part 5: Can we combine these vectors to get the zero vector? If possible, scale and add the vectors ā1, a2, and az to obtain the zero vector 0. If this is not possible, enter DNE. Use the names of vectors in your answer (e.g., enter 4a1 - 5a2 + a3 for 4a1 – 5a2 + a3). Do not enter coordinate representations such as (3, 4). = .
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