Results 1 to 4 of 4

Math Help - [SOLVED] Quick Communication Vector Question

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    27

    [SOLVED] Quick Communication Vector Question

    a) If u and v are non-zero vectors, but Proj(u onto v) = 0, what conclusion can be drawn?
    b) If Proj(u onto v) = 0, does it follow that Proj(v onto u) = 0? Explain.

    Small, clear explanation would be fine thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    v \ne 0\;\& \,proj_v u = \frac{{u \cdot v}}{{v \cdot v}}v\, \Rightarrow \,u \cdot v = 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    Vector and scalar product

    Hello narutoblaze
    Quote Originally Posted by narutoblaze View Post
    a) If u and v are non-zero vectors, but Proj(u onto v) = 0, what conclusion can be drawn?
    b) If Proj(u onto v) = 0, does it follow that Proj(v onto u) = 0? Explain.

    Small, clear explanation would be fine thanks
    (a) Use the scalar (dot) product formula to give the projection of \vec{u} onto \vec{v}, which is:

    proj( \vec{u} onto \vec{v}) =\frac{\vec{u}\cdot \vec{v}}{|\vec{v}|} = 0, |\vec{v}| \ne 0

    \Rightarrow \vec{u}\cdot \vec{v} = 0

    \Rightarrow |\vec{u}||\vec{v}|\cos\theta = 0, where \theta is the angle between the vectors \vec{u} and \vec{v}

    \Rightarrow \theta = \tfrac{\pi}{2}, since \vec{u} and \vec{v} are non-zero.

    So the vectors are perpendicular.

    (b) Yes: proj( \vec{v} onto \vec{u})= \frac{\vec{u}\cdot \vec{v}}{|\vec{u}|} = 0, |\vec{u}| \ne 0

    \Rightarrow \frac{\vec{u}\cdot \vec{v}}{|\vec{v}|} = 0

    \Rightarrow proj( \vec{u} onto \vec{v})= 0

    Grandad
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2009
    Posts
    27
    Much clearer, thanks Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quick Vector Field question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 5th 2010, 12:05 PM
  2. quick vector question
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 14th 2010, 07:40 AM
  3. Quick vector question
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 12th 2010, 03:45 AM
  4. Quick vector question
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 7th 2009, 12:02 PM
  5. quick vector field question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 23rd 2009, 01:42 PM

Search Tags


/mathhelpforum @mathhelpforum