A community for students.
Here's the question you clicked on:
 0 viewing
KonradZuse
 3 years ago
Do there exist scalars k and l such that the vectors u = (2,k,6) , v = (l,5,3) , and w = (1,2,3) are mutually orthogonal with respect to the Euclidean inner product?
KonradZuse
 3 years ago
Do there exist scalars k and l such that the vectors u = (2,k,6) , v = (l,5,3) , and w = (1,2,3) are mutually orthogonal with respect to the Euclidean inner product?

This Question is Closed

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0The answer says no, but I originally thought that since k and l were u2 and v1 that itonly matters the 3rd spot, but I realized that you do (u1v1w1) +etc....

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0Isn't it possible that we could find something = 0? Since that is what orthagonal means.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0Oh weait can scalars be negative?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if all three vectors were orthogonal, then:\[u\cdot w = 0\Longrightarrow (2)(1)+(k)(2)+(6)(3)=0\]\[2+2k+18=0\Longrightarrow 2k=20\Longrightarrow k=10\]Similarly,since v and w are orthogonal, we get that l must be 19.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes scalars can be negative.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0So we are actually solving for them...? I thought it was any number..

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0or those would be the numbers to = 0?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Since we are asking "does there exist", the question is asking "is there any one such number k and l." Its not the same as "for all/any k and l."

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0It doens't say 1 though? Or does that "mutually orthagonal" mean something?

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0Do there exist scalars k and l such that the vectors

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0If u and w are orthogonal, then k would have to be 10. If k is any other number, they wont be orthogonal since the inner/dot product wouldnt come out to zero.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0mutually orthogonal means that all three vectors are perpendicular to each other.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0The thing is, there is no way these three vectors can be mutually orthogonal. Since k would have to be 10, and l would have to be 19. Then u and v wouldnt be orhtogonal. There is no way to get all three to be perpendicular at the same time.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0I see, makes sense, thanks!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.