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Math Help - Find the correct Plane.

  1. #1
    Member grgrsanjay's Avatar
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    Find the correct Plane.

    Find the equation of the plane passing through the points (2,2,-1) and (3,4,2) and parallel to a line whose direction ratios are (7,0,6)

    Thanks in Advance
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Find the correct Plane!!

    A plane is determined by three points or by two direction vectors and a point, now you've given one direction vector and two points, so you need to find another direction vector.

    EDIT:
    Do you want a vector equation or a cartesian equation?
    Last edited by Siron; July 26th 2011 at 07:51 AM.
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  3. #3
    MHF Contributor Siron's Avatar
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    Re: Find the correct Plane!!

    Does this help you? Or? ...
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  4. #4
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    Re: Find the correct Plane!!

    Quote Originally Posted by grgrsanjay View Post
    Find the equation of the plane passing through the points (2,2,-1) and (3,4,2) and parallel to a line whose direction ratios are (7,0,6)
    A plane is parallel to a line if the direction of the line is perpendicular to the normal of the plane.

    <1,2,3>\times <7,0,2>=~?
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  5. #5
    Member grgrsanjay's Avatar
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    Re: Find the correct Plane!!

    Quote Originally Posted by Siron View Post
    Does this help you? Or? ...
    I need a Vector equation, I even need the steps please!
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Find the correct Plane!!

    This is the way I would do it:
    Given a plane \alpha and two points P_1 (2,2,-1) ,P_2 (3,4,2) \in \alpha and the plane is parallel to a line who's direction ratios are (7,0,6). In general the vector equation of a plane through one point P_1 and with two directions vectors R,Lis: P=P_1+kR+mL. Now we already have (we work now in a three dimensional space): (x,y,z)=(2,2,-1)+k(7,0,6)+mL. Can you determine the other direction vector L?
    .
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  7. #7
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    Re: Find the correct Plane!!

    Quote Originally Posted by grgrsanjay View Post
    I need a Vector equation, I even need the steps please!
    Define vectors:
    \begin{align*}  D&= <1,2,3> \\  P &=<2,2,-1>\\ R &=<x,y,z>\\ L&=<7,0,6>\end{align*}
    Note D=P_2-P_1

    Now the equation you want is
    (L\times D)\cdot (R-P)=0
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  8. #8
    Member grgrsanjay's Avatar
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    Re: Find the correct Plane!!

    Quote Originally Posted by Siron View Post
    This is the way I would do it:
    Given a plane \alpha and two points P_1 (2,2,-1) ,P_2 (3,4,2) \in \alpha and the plane is parallel to a line who's direction ratios are (7,0,6). In general the vector equation of a plane through one point P_1 and with two directions vectors R,Lis: P=P_1+kR+mL. Now we already have (we work now in a three dimensional space): (x,y,z)=(2,2,-1)+k(7,0,6)+mL. Can you determine the other direction vector L?
    .
    I Couldn't Understand it completely....But the Good thing is that i understood fully what Plato Explained

    So i think my problem is solved,
    Thanks
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: Find the correct Plane!!

    Ok , do you want to show me your solution?
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