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Math Help - Find the line

  1. #1
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    Find the line

    Find the line that is vertical to the plane 4x+y-3z=1 and passes through the point A(x0,y0,z0) of the plane so that z0=7.
    Could anyone help me with that exercise???
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  2. #2
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    Re: Find the line

    Quote Originally Posted by rikelda91 View Post
    Find the line that is vertical to the plane 4x+y-3z=1 and passes through the point A(x0,y0,z0) of the plane so that z0=7.
    I think that there is a translation problem here.
    By vertical to the plane you surely mean perpendicular to the plane. Do you not?
    And the line contains (x_0,y_0,7)~?

    Such a line looks like \\x=x_0+4t\\y=y_0+t\\z=7-3t
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  3. #3
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    Re: Find the line

    You can do a bit more than that. If (x_0, y_0, 7) lies on the plane 4x+ y- 3z= 1 then [tex]4x_0+ y_0- 21= 1 so that y_0= 22- x_0 and you can write the line as x= x_0+ 4t, y= 22- x_0+ t, and z= 7- 3t.
    Thanks from rikelda91
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  4. #4
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    Re: Find the line

    Hello, rikelda91!

    This is a strange problem.
    Do you have the answer?


    \text{Find the line that is vertical to the plane }4x+y-3z\:=\:1
    . . \text{and passes through the point }A(x_o,y_o,7)\text{ of the plane.}

    \text{The direction of the line is the normal to the plane: }\,\vec n \,=\,\langle 4,1,\text{-}3\rangle

    \text{Since point }A\text{ is on the plane: }\:4x_o + y_o - 3(7) \:=\:1 \quad\Rightarrow\quad y_o \,=\,22-4x_o

    \text{We have point }A(x_o,\,22\!-\!4x_o,\,7)\,\text{ and vector }\,\vec n \,=\,\langle 4,1,\text{-}3\rangle


    \text{The line is: }\:\begin{Bmatrix}x &=& x_o + 4t \\ y &=& (22\!-\!4x_o) + t \\ z &=& 7 - 3t \end{Bmatrix}
    Thanks from rikelda91
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  5. #5
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    Re: Find the line

    no I don't have the answer :/ ..actually I meant perpendicular to the plane...
    the line equation should be l(t)=a+tu (u is a parallel vector to the line). So l(t)=(x0,22-4x0,7) +t(4,1,-3)
    Right???
    Last edited by rikelda91; August 20th 2013 at 07:26 AM.
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