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Math Help - Help with a question about Planes

  1. #1
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    Help with a question about Planes

    I cannot get the correct answer to this question..any help would be greatly appreciated. Thanks in advance

    Let P1 be the plane defined by:
    (-2,0,2), (5,-1,5) and (0,2,4)

    Find the equation of the plane perpendicular to P1 and containing the line:
    (x,y,z)=(0,-1,-3)+ t(-1,3,-3)

    Answer should be in the form Ax+By+Cz-D=0

    So first i found the equation for plane P1 as -8x-8y+16z-48=0
    I do not really know where to go from here.
    thanks
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  2. #2
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    Quote Originally Posted by kblythe View Post
    I cannot get the correct answer to this question..any help would be greatly appreciated. Thanks in advance

    Let P1 be the plane defined by:
    (-2,0,2), (5,-1,5) and (0,2,4)

    Find the equation of the plane perpendicular to P1 and containing the line:
    (x,y,z)=(0,-1,-3)+ t(-1,3,-3)

    Answer should be in the form Ax+By+Cz-D=0

    So first i found the equation for plane P1 as -8x-8y+16z-48=0
    I do not really know where to go from here.
    thanks

    So dividing by -8 we get that P_1:\,\,x+y-2z+8=0\,\Longrightarrow\,(1,1,-2) is a normal (and thus perpendicular) vector to P_1, so the wanted plane must contain, choosing t = 0 and t = 1 for the line, the vectors (1,1,-2)\,,\,(0,-1,-3)\,,\,\,(-1,2,-6), so plugging this in Ax+By+Cz+D=0 and solving the system we get A=-\frac{9}{5}C\,,\,\,B=\frac{2}{5}C\,,\,\,D=17 , and the wanted plane is (taking 5C) : -9x+2y+5z+17=0.

    Check this

    Tonio
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  3. #3
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    hey thanks for the reply. the only part i am still confused about is that in the question it says it wants it in the form with minus D (Ax+By+Cy - D=0) and in your answer you have +17. Is that ok? or am i supposed to change my answer in some way to account for this?
    thanks
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  4. #4
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    Quote Originally Posted by kblythe View Post
    hey thanks for the reply. the only part i am still confused about is that in the question it says it wants it in the form with minus D (Ax+By+Cy - D=0) and in your answer you have +17. Is that ok? or am i supposed to change my answer in some way to account for this?
    thanks
    Then multiply the entire equation by -1! -1(-9x+2y+5z+17)=-1(0) so 9x- 2y- 5z- 17= 0.
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