Determining Orthogonal Vectors

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Feb 10, 2022.

  1. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Section 6.4

    Can you do 56 in detail? Thanks.

    Screenshot_20220206-121825_Samsung Notes.jpg
     
    nycmathguy, Feb 10, 2022
    #1
  2. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    56.

    two vectors are perpendicular to each other if the dot product of the two vectors is zero

    u= <cos(θ),sin(θ)>
    v= <sin(θ),−cos(θ)>

    Calculate

    u*v
    = <cos(θ),sin(θ)> *<sin(θ),−cos(θ)>
    =<cos(θ)*sin(θ) +sin(θ)(−cos(θ))>
    =<cos(θ)*sin(θ) -sin(θ)(cos(θ))>
    =0

    => vectors u and v are orthogonal
     
    MathLover1, Feb 11, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Thanks. I will do the rest this weekend.
     
    nycmathguy, Feb 11, 2022
    #3
  4. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Please visit the link below. How is 44 done using vectors not the law of cosines as suggested by Country Boy?

    Find Angles in a Triangle
     
    nycmathguy, Feb 12, 2022
    #4
  5. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422

    IMG_20220212_191948.jpg

    IMG_20220212_191957.jpg

    IMG_20220212_192006.jpg
     
    nycmathguy, Feb 13, 2022
    #5
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads
There are no similar threads yet.
Loading...