Results 1 to 7 of 7

Math Help - perpendicular vectors

  1. #1
    Junior Member
    Joined
    Nov 2008
    From
    Vermont, New England, USA, North America, Earth, Sol Solar System, Orion Arm, Milky Way Galaxy
    Posts
    61

    perpendicular vectors

    No idea how to do this, all I know is you need the dot product.
    Find two vectors V1 and V2 whose sum is <-4,3,0>, where V1 is parallel to and V2 is perpendicular to <-3,-1,5>.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by jahichuanna View Post
    No idea how to do this, all I know is you need the dot product.
    Find two vectors V1 and V2 whose sum is <-4,3,0>, where V1 is parallel to and V2 is perpendicular to <-3,-1,5>.
    This is a truly messy and tedious problem.
    Let v_1=<a,b,c>~\&~v_2=<\alpha a, \alpha b, \alpha c>.
    Then the perpendicular part gives -3a-b+5c=0.

    From that you get four equations in four variables. Solve it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2008
    From
    Vermont, New England, USA, North America, Earth, Sol Solar System, Orion Arm, Milky Way Galaxy
    Posts
    61
    Quote Originally Posted by Plato View Post
    This is a truly messy and tedious problem.
    Let v_1=<a,b,c>~\&~v_2=<\alpha a, \alpha b, \alpha c>.
    Then the perpendicular part gives -3a-b+5c=0.

    From that you get four equations in four variables. Solve it.
    I still have no idea where to go. I cant even get started. can you please guide me all the way through it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by jahichuanna View Post
    I still have no idea where to go. I cant even get started. can you please guide me all the way through it?
    Understand, I will not do this for you.
    Here is the set up.
    \left\{ \begin{gathered}  (\alpha  + 1)a =  - 4 \hfill \\  (\alpha  + 1)b =  - 1 \hfill \\  (\alpha  + 1)c = 0 \hfill \\   - 3a - b + 5c = 0 \hfill \\ \end{gathered}  \right.

    Solve for a,~b,~c,~\&,\alpha

    Again, do not ask me to do it.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2008
    From
    Vermont, New England, USA, North America, Earth, Sol Solar System, Orion Arm, Milky Way Galaxy
    Posts
    61
    Quote Originally Posted by Plato View Post
    Understand, I will not do this for you.
    Here is the set up.
    \left\{ \begin{gathered}  (\alpha  + 1)a =  - 4 \hfill \\  (\alpha  + 1)b =  - 1 \hfill \\  (\alpha  + 1)c = 0 \hfill \\   - 3a - b + 5c = 0 \hfill \\ \end{gathered}  \right.

    Solve for a,~b,~c,~\&,\alpha

    Again, do not ask me to do it.
    understood. but I'm not clear on how exactly you got those equations
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by jahichuanna View Post
    understood. but I'm not clear on how exactly you got those equations
    You do not understand the question. Do you?
    In which case how do you expect to get any help?
    I am done with this thread.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Mar 2010
    Posts
    107
    How does he not expect help..? You could help him understand the question of course...

    Okay so I'm assuming you know how to do cross products.

    Let \vec{a} = \vec{V_1} and \vec{b} = \vec{V_2} and \vec{a} = <a_1,a_2,a_3> and \vec{b}=<b_1,b_2,b_3>

    Then it says the sum of the two vectors is <-4,3,0>. so

    <a_1 + b_1,a_2 + b_2,a_3 + b_3> = <-4,3,0>

    a_1+b_1=-4
    a_2+b_2=3
    a_3+b_3=0

    Then it says the first vector is parallel to <-3,-1,5>, so we use the dot product: \vec{b}      \bullet <-3,-1,5> = 0


    \vec{b} * <-3,-1,5> = 0
    -3b_1-b_2+5b_3=0

    Now the cross product. The theory is that \vec{a}    \times <-3,-1,5> = \vec{0}

    Doing that will give you three more equations. Solve for a_1 for a_2 and a_3 for a_2. Finally, plug those values in the first 3 equations. Then, solve for b_1, b_2, and b_3 and plug into the equation we got from the dot product.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Perpendicular Vectors
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 4th 2011, 04:21 PM
  2. Perpendicular vectors
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 7th 2011, 03:03 PM
  3. Vectors (Perpendicular vectors) problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 30th 2010, 09:45 AM
  4. Perpendicular vectors
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: October 25th 2009, 11:03 AM
  5. Perpendicular Vectors
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 31st 2009, 05:13 PM

Search Tags


/mathhelpforum @mathhelpforum