A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

egbeach

  • one year ago

Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <6, -2>, v = <8, 24>

  • This Question is Closed
  1. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the vectors are orthogonal if the result is 0 after using the dot product. \[u \cdot v =<u_1v_1,u_2v_2,...u_nv_n> \]

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If vectors are parallel, then there exists a scalar \(c\) such that\[ \mathbf u = c \mathbf v \]

  3. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[u \cdot v = <u_1v_1+u_2v_2+...u_nv_n>\] for dot product but if it's neither than the dot product can't be 0 and a scalar c doesn't exist.

  4. egbeach
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do i just plug in the numbers to solve?

  5. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you could.. since we have \[u=<u_1,u_2>, v=<v_1,v_2>\] and we can use dot product \[u \cdot v = <u_1v_1+u_2v_2+...u_nv_n> \]

  6. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    u= <6,-2> and v = <8,24> \[u_1=6,u_2=-2,v_1=8,v_2=24 \] now we plug those values into the dot product formula \[u \cdot v = u_1v_1+u_2v_2\]

  7. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[u \cdot v = (6)(8)+(-2)(24) \]

  8. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so what is 6 x 8 and what is -2 x 24 ?

  9. egbeach
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    6x8=48 -2x24= -48

  10. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    mhm \[u \cdot v = 48-48 \] so now what's 48-48?

  11. egbeach
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0. so is it neither?

  12. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    no.. since our dot product is 0, our vectors are _______________

  13. egbeach
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    orthogonal since it equal 0

  14. UsukiDoll
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes :)

  15. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.