Results 1 to 5 of 5

Math Help - planes, intersections and angles

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    91

    planes, intersections and angles



    hey... i have worked out the cross product vector and i get (-1, 3, -3)

    and the vector equation of the line that i got is (x,y,z)= (1,2,-1) + t(-1,3,-3)
    which i think is correct....

    am i correct??? and if so or not..how do i go on about working out question c and d??

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by b00yeah05 View Post


    hey... i have worked out the cross product vector and i get (-1, 3, -3)

    and the vector equation of the line that i got is (x,y,z)= (1,2,-1) + t(-1,3,-3)
    which i think is correct....

    am i correct??? and if so or not..how do i go on about working out question c and d??

    thanks
    Hi,

    1. I've got as the result of the cross product: [-1, -3, -7]

    2. Therefore the equation of the common line would be: [x,y,z] = [1,2,-1] + t[-1, -3, -7]

    3. The angle between 2 planes is equal to the angle between the normal vectors of the planes. Use the the definition of the dot product to calculate the angle.
    If the angle between the planes is called \alpha then I've got:

    \cos(\alpha) = \frac{[1,2,-1] \cdot [2,-3,1]}{\sqrt{6} \cdot \sqrt{14}}~\implies~ \alpha \approx 123.06^\circ
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2008
    Posts
    91
    hey..i made a mistake on the cross product so i got -3 but i fixed it and now have -7 also...but does ur working answer the question to part c??? as it says use this information and answer from part b to find vector equation to find line of intersection of plane 1 and plane 2??? why have you only used one plane??? in this case plane 2??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by b00yeah05 View Post
    hey..i made a mistake on the cross product so i got -3 but i fixed it and now have -7 also...but does ur working answer the question to part c??? as it says use this information and answer from part b to find vector equation to find line of intersection of plane 1 and plane 2??? why have you only used one plane??? in this case plane 2??
    1. The cross product of the 2 normal vector will yield the direction vector of the line of intersection. That means we know the direction of the line.

    2. If the point x_0 lies on both planes it must lie on the line of intersection. With one point and the direction vector the line is determined completely.

    3.
    why have you only used one plane??? in this case plane 2??
    I don't understand what you mean here.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2008
    Posts
    91
    yeah..sorry..i was confused a bit myself after i read that, but never the less..i understand what you did and i tried doing it again and i ended up with teh same answer..so thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Angles between planes
    Posted in the Calculus Forum
    Replies: 8
    Last Post: September 14th 2011, 01:23 PM
  2. Angle between planes and line of intersection of planes.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 6th 2011, 12:08 PM
  3. Vector Q - Planes and angles
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 4th 2010, 03:15 AM
  4. Finding the intersections of 3D planes
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: August 22nd 2009, 06:54 PM
  5. Intersections of 3 Planes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 27th 2008, 10:52 PM

Search Tags


/mathhelpforum @mathhelpforum