Write i = [1 – 2 1]" as the addition of two vectors. One of them should be perpendicular to ū = [1 2 – 7]" and the other should be parallel to to w = [1 2 – 7]".
Write i = [1 – 2 1]" as the addition of two vectors. One of them should be perpendicular to ū = [1 2 – 7]" and the other should be parallel to to w = [1 2 – 7]".
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
question d only
![(a) Find the angle between i = [1 – 2 1]2 and w
= [1 2 – 7)".
-
-
(b) Using the same vectors i and w as above, compute projo(T).
(c) Show, using the definition of projection and the algebraic properties of dot product, that
for any two non-zero vectors ā and b you have that (b– proja(b)) · a = 0.
This shows that any vector b in R", can be written as the addition of a vector perpen-
dicular to a given vector a plus a vector parallel to ā.
T
(d)
Write i = [1 –-2 1]' as the addition of two vectors. One of them should be perpendicular
to w = [1 2 – 7]" and the other should be parallel to to w = [1 2 – 7]".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa45503fd-7bc5-487c-b378-e4ef26c41205%2F3edc374e-aec2-4fb9-bef0-4cc2888f0cde%2Fjfchx8j_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Find the angle between i = [1 – 2 1]2 and w
= [1 2 – 7)".
-
-
(b) Using the same vectors i and w as above, compute projo(T).
(c) Show, using the definition of projection and the algebraic properties of dot product, that
for any two non-zero vectors ā and b you have that (b– proja(b)) · a = 0.
This shows that any vector b in R", can be written as the addition of a vector perpen-
dicular to a given vector a plus a vector parallel to ā.
T
(d)
Write i = [1 –-2 1]' as the addition of two vectors. One of them should be perpendicular
to w = [1 2 – 7]" and the other should be parallel to to w = [1 2 – 7]".
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