Results 1 to 2 of 2

Math Help - Mathematics for aplications development.

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    1

    Mathematics for aplications development.

    Hi,

    im doing test revision. Could someone take me through the steps to solving these two questions, the actuall answers and working isnt important, these are just random questions on a revision sheet and having left my notes at uni i have nothing to look at to help me.

    The plane 3x-y+z=0 passes through the origin. Find the reflection, in this plane, of the point P(4,-3,0)

    and

    Calculate the perpendicular distance between the planes r.(4i-3j+k)=10 and 4x-3y+z=8

    thank you very much for your time!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,417
    Thanks
    1330
    Quote Originally Posted by EpicOfX View Post
    Hi,

    im doing test revision. Could someone take me through the steps to solving these two questions, the actuall answers and working isnt important, these are just random questions on a revision sheet and having left my notes at uni i have nothing to look at to help me.

    The plane 3x-y+z=0 passes through the origin. Find the reflection, in this plane, of the point P(4,-3,0)
    Call the reflection point Q= (a, b, c). Then the line PQ is perpendicular to the plane and P and Q are equi-distant from the plane.

    The plane has "normal vector" <3, -1, 1> and so the perpendicular line through P has parametric equations x= 3t+ 4, y= -t- 3, z= t. Put those for into the equation of the plane to find the point where the line intersects the plane. Find the distance from P to that point and then find the point on the line the same distance on the other side of the plane.

    and

    Calculate the perpendicular distance between the planes r.(4i-3j+k)=10 and 4x-3y+z=8

    thank you very much for your time!
    I take it that r= xi+ yj+ zk so "r.(4i-3j+ k)= 10" is 4x- 3y+ z= 10. Notice that the coefficients of the two planes are the same so the two planes are parallel and there is a common perpendicular. Take any point on the first plane. Since z= 10- 4x+ 3y, taking x= 1, y= -1 gives z= 10-4-3= 3 so (1, -1, 3) is a point on the first plane. A line perpendicular to the plane, through that point, has parametric equations x= 4t+ 1, y= -3t- 1, z= t+ 3. Put those into the equation for the second plane, 4x- 3y+ z= 8, to find
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Taylor development
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 30th 2011, 07:11 AM
  2. Taylor development
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 27th 2009, 11:08 AM
  3. Mathematics: Discrete-Mathematics (Algorithems)
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 2nd 2008, 06:27 AM
  4. Optimization. (aplications of differentiation)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 20th 2007, 12:19 PM
  5. shapes development
    Posted in the Geometry Forum
    Replies: 0
    Last Post: January 16th 2006, 10:11 AM

Search Tags


/mathhelpforum @mathhelpforum