Results 1 to 5 of 5

Math Help - Vector Proofs

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    4

    Vector Proofs

    Ive tried this problem numerous times but im constantly going in circles. Not looking for the answer because that would defeat the purpose of doing this question, more for just a small hint if possible

    ABCD is a rectangle. Prove OA OC = OB OD
    where OA, OC, OB and OD are all vectors.

    point O is an origin NOT on the same plane as the rectangle. any help is appreciated. thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by Finroe View Post
    Ive tried this problem numerous times but im constantly going in circles. Not looking for the answer because that would defeat the purpose of doing this question, more for just a small hint if possible

    ABCD is a rectangle. Prove OA · OC = OB · OD
    where OA, OC, OB and OD are all vectors.

    point O is an origin NOT on the same plane as the rectangle. any help is appreciated. thanks
    Although this might not help you, I would recommend thinking of it like a pyramid with a rectangular base, and O is the top of that pyramid (vertex).

    Just to get a visual...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by Finroe View Post
    Ive tried this problem numerous times but im constantly going in circles. Not looking for the answer because that would defeat the purpose of doing this question, more for just a small hint if possible

    ABCD is a rectangle. Prove OA OC = OB OD
    where OA, OC, OB and OD are all vectors.

    point O is an origin NOT on the same plane as the rectangle. any help is appreciated. thanks
    Hello,

    as you requested: Only a hint:

    \overrightarrow{OA}=\overrightarrow{OB}+\overright  arrow{BA}

    \overrightarrow{OC}=\overrightarrow{OB}+\overright  arrow{BC}

    Multiply the RHSs of these equations. One of the summands is zero because you have to do with a rectangle with orthogonal sides(?). You can factor the sum. That's it

    EB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2006
    Posts
    4
    First off, thanks for the prompt replies. Ive used the hints and theyve been very helpful. i overlooked the fact that two perpindicular vectors have a dot product of 0, our dot product unit was a while ago. I was just wondering, if anyone has tried solving this problem and if they have, how long is their solution. My proof is close to 3/4 of a page and i still havent proved the equality. let me know if you managed to solve this and how logn the proof was. thanks again.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by Finroe View Post
    First off, thanks for the prompt replies. Ive used the hints and theyve been very helpful. i overlooked the fact that two perpindicular vectors have a dot product of 0, our dot product unit was a while ago. I was just wondering, if anyone has tried solving this problem and if they have, how long is their solution. My proof is close to 3/4 of a page and i still havent proved the equality. let me know if you managed to solve this and how logn the proof was. thanks again.
    Hello,

    I repeat my hint:

    \overrightarrow{OA}=\overrightarrow{OB}+\overright  arrow{BA}

    \overrightarrow{OC}=\overrightarrow{OB}+\overright  arrow{BC}

    According to your problem you'll get the equuation:

    \overrightarrow{OA} \cdot \overrightarrow{OC}=\left( \overrightarrow{OB}+\overrightarrow{BA} \right) \cdot \left( \overrightarrow{OB}+\overrightarrow{BC} \right)

    Expand the RHS:

    \overrightarrow{OA} \cdot \overrightarrow{OC}=\overrightarrow{OB} \cdot \overrightarrow{OB}+\overrightarrow{OB} \cdot \overrightarrow{BC} +\overrightarrow{BA} \cdot \overrightarrow{OB} +\underbrace{\overrightarrow{BA} \cdot \overrightarrow{BC}}_{\text{equals zero}}

    Factor the RHS:

    \overrightarrow{OA} \cdot \overrightarrow{OC}=\overrightarrow{OB} \cdot  \underbrace{\left( \overrightarrow{OB} + \overrightarrow{BC} + \overrightarrow{BA} \right)}_{equals\  \overrightarrow{OD}}

    Notice please that with vectors the following equation is true:
    \overrightarrow{BA}=\overrightarrow{CD}

    Thus:

    \overrightarrow{OA} \cdot \overrightarrow{OC}=\overrightarrow{OB} \cdot \overrightarrow{OD}

    EB
    Attached Thumbnails Attached Thumbnails Vector Proofs-vektor_rechteck.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector proofs for triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 30th 2010, 12:24 AM
  2. vector space proofs
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 18th 2009, 04:27 AM
  3. vector space proofs
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 4th 2009, 03:36 PM
  4. Need some help, vector proofs
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 21st 2006, 10:17 AM
  5. Vector Proofs
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 15th 2005, 10:49 PM

Search Tags


/mathhelpforum @mathhelpforum