Results 1 to 5 of 5

Math Help - Gr 12. Vector Question Involving Dot Product of Two Vectors

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    27

    Gr 12. Vector Question Involving Dot Product of Two Vectors

    This is one of the difficult question in this chapter.

    The vectors a = 3i - 4j - k (3, -4, -1) and b = 2i + 3j -6k (2, 3, -6) are the diagonals of a parallelogram. Show that this parallelogram is a rhombus, and determine the lengths of the sides and the angles between the sides.

    Yes, I know what a rhombus is and some of it's properties.
    I used the dot product for the 2 Vectors given which = 0 therefore I know that the 2 vectors bisect each other in the rhombus. So, how do I find the side lengths and the angle? Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,125
    Thanks
    1009
    s = \sqrt{\left(\frac{|a|}{2}\right)^2 + \left(\frac{|b|}{2}\right)^2}

    \theta = 2\arctan\left(\frac{|a|}{|b|}\right)

    \phi = 2\arctan\left(\frac{|b|}{|a|}\right)<br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    Posts
    27
    Thanks dude for not giving the answer! After taking a closer look at it I understood how you got the Side equation! But No idea how use arctan since we don't learn that in high school but I used tan instead given that it's right triangles and got the correct angles. Thanks sooo much! Speedy and Fast!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Suppose that u & v are two vectors that form the adjacent forming the sides of the parallelogram.
    Then we know that a = u - v\;\& \;b = u + v or visa versa.
    Thus we have u = \frac{{a + b}}{2}\;\& \;v = \frac{{a - b}}{2}. Now use the given to prove that \left\| u \right\| = \left\| v \right\|.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2009
    Posts
    27
    Thanks Plato for the extra info!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proove involving dot product and zero vector
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 10th 2010, 08:16 AM
  2. Replies: 2
    Last Post: February 17th 2009, 06:29 PM
  3. Replies: 2
    Last Post: February 17th 2009, 04:27 PM
  4. Question involving vectors
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 5th 2008, 05:12 AM
  5. Strange question involving vectors
    Posted in the Calculus Forum
    Replies: 0
    Last Post: February 5th 2008, 05:10 AM

Search Tags


/mathhelpforum @mathhelpforum