Results 1 to 3 of 3

Thread: vectors: are these valid?

  1. #1
    Member
    Joined
    Aug 2007
    Posts
    239

    vectors: are these valid?

    If $\displaystyle \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} $ does it follow that $\displaystyle \vec{b} = \vec{c} $?

    I said that $\displaystyle \vec{a} \cdot (\vec{b}- \vec{c}) = 0 $ which means that they are perpendicular which implies that $\displaystyle \vec{b} \neq \vec{c} $.


    If $\displaystyle \vec{a} \times \vec{b} = \vec{a} \times \vec{c} $ does it follow that $\displaystyle \vec{b} = \vec{c} $?

    I said that $\displaystyle \vec{a} \times (\vec{b} - \vec{c}) = 0 $ which means that they are parallel, and so $\displaystyle \vec{b} \neq \vec{c} $.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by shilz222 View Post
    If $\displaystyle \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} $ does it follow that $\displaystyle \vec{b} = \vec{c} $?

    I said that $\displaystyle \vec{a} \cdot (\vec{b}- \vec{c}) = 0 $ which means that they are perpendicular which implies that $\displaystyle \vec{b} \neq \vec{c} $.
    actually, this means the vector $\displaystyle \vec {a}$ is perpendicular to the vector $\displaystyle \vec{b} - \vec {c}$. it does not say anything about the vectors $\displaystyle \vec{b}$ and $\displaystyle \vec{c}$ or how they relate to each other.

    If $\displaystyle \vec{a} \times \vec{b} = \vec{a} \times \vec{c} $ does it follow that $\displaystyle \vec{b} = \vec{c} $?

    I said that $\displaystyle \vec{a} \times (\vec{b} - \vec{c}) = 0 $ which means that they are parallel, and so $\displaystyle \vec{b} \neq \vec{c} $.
    a similar observation can be made here
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,782
    Thanks
    2824
    Awards
    1
    Because both are false, find counter examples, such as:
    $\displaystyle A = \left\langle {1,1,1} \right\rangle ,\;B = \left\langle {1,0, - 1} \right\rangle ,\;C = \left\langle { - 1,1,0} \right\rangle ,\;\& \;A \cdot B = A \cdot C$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. is a≡b still valid??
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Oct 13th 2010, 06:36 PM
  2. Is this a Valid proof? [Vectors]
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: Nov 8th 2009, 11:14 AM
  3. valid,non valid arguments
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Sep 8th 2009, 06:12 PM
  4. Is this valid?
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: May 7th 2009, 05:38 AM
  5. Is this valid?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jan 31st 2009, 04:28 PM

Search Tags


/mathhelpforum @mathhelpforum