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Math Help - Find parallel Vector

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    Find parallel Vector

    Can somebody help with this. I am finding it confusing. Not too good with this vector stuff.

    Determine if the plane given by -x+2z=10 and the line given by vector r=<5,2-t,10+4t> are orthogonal, parallel or neither.


    In particular, how do I find a line parallel to vector r?
    Last edited by p75213; October 7th 2010 at 02:36 AM. Reason: formatting
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    A line is perpendicular to a plane if its direction is parallel to the normal.
    A line is parallel to a plane if its direction is perpendicular to the normal.

    So work with D=<0,-1,4>~\&~N=<-1,0,2>.
    Are they perpendicular or parallel?
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    How did you derive D?
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    Quote Originally Posted by p75213 View Post
    How did you derive D?
    If the line r(t)=<a+ut,b+vt,c+wt> then its direction vector is D=<u,v,w>.
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    Quote Originally Posted by p75213 View Post
    Can somebody help with this. I am finding it confusing. Not too good with this vector stuff.

    Determine if the plane given by -x+2z=10 and the line given by vector r=<5,2-t,10+4t> are orthogonal, parallel or neither.


    In particular, how do I find a line parallel to vector r?

    If Ax+By+Cz+D=0 is some plane, the perpendicular victor to this plane is the vector (A,B,C), in your case (0,-1,4)

    r=<5,2-t,10+4t> is a line, with vector direction (0,-1,4).

    If the dot product of above two vectors is equals to zero then the line and the plane are orthogonal.

    If two vectors have linear dependency then they are parallel.
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