Results 1 to 4 of 4

Math Help - Parallelogram and Vectors

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    43

    Parallelogram and Vectors

    A Parallelogram with sides of equal length is called a rhombus. Show that the diagonals of a rhombus are perpendicular.

    So, I start with v and u which are perpendicular vectors. v + w is a diagonal of the rhombus.

    I am not sure how to get the other one, or to solve this question, really.

    I know that in order for two vectors to be perpendicular then the dot product must be 0.

    so I guess, I need both diagonals and to see if their dot product is zero?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,708
    Thanks
    1638
    Awards
    1
    Quote Originally Posted by zodiacbrave View Post
    A Parallelogram with sides of equal length is called a rhombus. Show that the diagonals of a rhombus are perpendicular.
    Suppose that \overrightarrow a \;\& \,\overrightarrow b are adjacent sides of thee rhombus.
    Then the diagonals are \overrightarrow a  + \overrightarrow b \;\& \,\overrightarrow a  - \overrightarrow b .
    Now look at the dot product, \left( {\overrightarrow a  + \overrightarrow b } \right) \cdot \left( {\overrightarrow a  - \overrightarrow b } \right) = ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2008
    Posts
    43
    Thank you for your reply..

    I know (a + b) is just a regular vector but the fact that we are labeling it as the sum of two other vectors is confusing to me. What I mean is, if vector a has components (a1, a2) and vector b has components (b1, b2) then won't the dot product of (a + b) and (a - b)
    equal (a1)^2 - (b1)^2 + (a2)^2 - (b2)^2

    I guess, I am not understanding the actual method of proving it algebraically.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,708
    Thanks
    1638
    Awards
    1
    Quote Originally Posted by zodiacbrave View Post
    I know (a + b) is just a regular vector but the fact that we are labeling it as the sum of two other vectors is confusing to me. What I mean is, if vector a has components (a1, a2) and vector b has components (b1, b2) then won't the dot product of (a + b) and (a - b)
    equal (a1)^2 - (b1)^2 + (a2)^2 - (b2)^2
    Recall that \vec{p}\cdot\vec{p}=\left\| p \right\|^2

    (\vec{a}+\vec{b})\cdot(\vec{a}-\vec{b})=\vec{a}\cdot\vec{a}-\vec{b}\cdot\vec{b}=0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Parallelogram vectors
    Posted in the Geometry Forum
    Replies: 3
    Last Post: September 25th 2010, 09:59 AM
  2. Parallelogram with Vectors
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 22nd 2009, 06:53 AM
  3. parallelogram using vectors
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 15th 2009, 03:42 PM
  4. Parallelogram in vectors
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 24th 2009, 04:50 AM
  5. Proof in Parallelogram using vectors
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 14th 2006, 11:06 AM

Search Tags


/mathhelpforum @mathhelpforum