Results 1 to 7 of 7

Math Help - Vectors - parallelepiped volume

  1. #1
    Member
    Joined
    Feb 2008
    Posts
    97

    Vectors - parallelepiped volume

    I think this is a parallelogram prism?

    This is the components given:

    vectors:

    a=(2, -5, -1)
    b=(3,0,1)
    c=(3,-1,-1)

    So, I thought if this was a parallel prism, find a cross-product b, get the magnitude (area of parallelogram) and then multiply by magnitude of the third vector (depth?). But I get the wrong answer. I'm getting 71, the answer is 29. Any help?
    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 theowne View Post
    I think this is a parallelogram prism?

    This is the components given:

    vectors:

    a=(2, -5, -1)
    b=(3,0,1)
    c=(3,-1,-1)

    So, I thought if this was a parallel prism, find a cross-product b, get the magnitude (area of parallelogram) and then multiply by magnitude of the third vector (depth?). But I get the wrong answer. I'm getting 71, the answer is 29. Any help?
    i keep getting 25. are you sure you typed the vectors correctly?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2008
    Posts
    97
    You're right, I typed wrong, the correct vector for b is (4,0,1). Er, can you tell me what steps you took?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Just take the determinant of your vectors. You will get -29. Of course, we need the absolute value.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    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 theowne View Post
    You're right, I typed wrong, the correct vector for b is (4,0,1). Er, can you tell me what steps you took?
    i did what galactus suggested.

    the volume is given by V = \left| \begin{array}{ccc} 4 & 0 & 1 \\ 2 & -5 & - 1 \\ 3 & - 1 & -1 \end{array}\right| .........of course i mean the determinant of that matrix

    and also as galactus said, if you get a negative answer, just take the absolute value
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Also, a\cdot{(b\times{c})} will give you the same thing.

    Take the cross product of b and c. Then dot product that with a.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Feb 2008
    Posts
    97
    But how does that relate with the question? How are those equations related to finding the volume of a parallelepiped, what does each part represent? Why are you doing bxc dot product with a? To start, am I right that this is a parallelogram prism?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Getting the volume of a parallelepiped defind by 3 R^4 Vectors
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 31st 2011, 06:55 AM
  2. Rectangular parallelepiped vectors, etc
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 22nd 2011, 07:38 AM
  3. Vectors: parallelepiped
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 6th 2011, 05:58 AM
  4. [SOLVED] Find volume of a parallelepiped with 3 sides
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 4th 2010, 02:09 PM
  5. volume of parallelepiped w/ adjacent edges
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 24th 2009, 01:26 PM

Search Tags


/mathhelpforum @mathhelpforum