anonymous
  • anonymous
Find an equation of the plane containing points R(1,2,3), T(-3,2,3), M(2,0,5). So I got 0x+y+z=5 Then, find the distance from the place in #9 to point S(-1,2,5). Where do I go from here?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
how did you obtain the equation of the plane
anonymous
  • anonymous
found the vector RT = <-4,0,0> and vector RM = <1,-2,2> then did the cross product to get 0i+8j+8k. Then I did vector RM (dot) <0,8,8> which is how I got 0x+1y+1z=5
anonymous
  • anonymous
was there a simpler way to do it?

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anonymous
  • anonymous
yeah if you were give three points in (x1,y1,z1) (x2,y2,z2) (x3,y3,z3) the determinant with first row x-x1 y-y1 z-z1 second row x2-x1 y2-y1 z2-z1 third row x3-x1 y3-y1 z3-z1 will give you the equation of the plane and the distance between a plane and a point D=(|ax0 +by0+cz0+d| )/sqrt(a^2+b^2+c^2) where a b c are the direction cosines of the plane in the normal form and x0 y0 z0 are coordinates of the point
anonymous
  • anonymous
i still dont understand sorry :(
anonymous
  • anonymous
|dw:1378231768708:dw|
anonymous
  • anonymous
that will give you the equation of the plane passing through three points (x1,y1,z1) (x2,y2,z2) (x3,y3,z3)
anonymous
  • anonymous
\[|ax _{0}+by_{0}+cz_{0}+d| / \sqrt{a^2 +b^2+c^2}\]
anonymous
  • anonymous
is the equation that will give you the shortest distance between a point (x0,y0,z0) and a plane ax+by+cz+d=0
anonymous
  • anonymous
ok using your diagram I got x-1, y-2, z-3, etc but I am confused as to how to use this in the equation ax_0? thank you for your help!!!
anonymous
  • anonymous
the diagram is to find the equation of the plane which you already did i just stated an easier way to do it now you have a point S(-1,2,5) and a plane 0x+y+z-5=0 here x0 = -1 y0 = 2 z0 = 5 and a, b,c,d are 0,1,1,-5 respectively substitute them in the equation of shortest distance between a plane and a point and you will get the answer
anonymous
  • anonymous
btw you know how to evaluate a determinant right?
anonymous
  • anonymous
no
anonymous
  • anonymous
do you know what a matrix is?
anonymous
  • anonymous
yes
anonymous
  • anonymous
on substituting the values this is how it'll look (0)(-1) +(1)(2) +(1)(5) -5 /square root of (0)^2+(1)^2+(1)^2
anonymous
  • anonymous
ohh ok. thank you :)
anonymous
  • anonymous
did you get it
anonymous
  • anonymous
yes i got 2/root(2)
anonymous
  • anonymous
yep you got it
anonymous
  • anonymous
thanks!!
dumbcow
  • dumbcow
@Aenn88 , for future reference http://en.wikipedia.org/wiki/Plane_(geometry)#Defining_a_plane_through_three_points
anonymous
  • anonymous
thanks for the link! thats not anywhere in my book. so much more simple
dumbcow
  • dumbcow
:)

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