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Homework Help: Finding Vector Equation

  1. Sep 22, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the vector equation with parameter T that passes through the point (6,0,1) and is perpendicular to the plane x+4y+6z = 5

    3. The attempt at a solution
    So i'm looking for the direction numbers n (a,b,c) for whatever direction is perpendicular to the plane given x+4y+6z = 5

    What if I try to take the dot product of i+4j+6k with xi+yj+zk and solve for when it equals zero. The problem with doing that is there are more than one possible answers that solve that. Also since x+4y+6z = 5 is the linear equation of a plane i'm not even sure i'm thinking about this right at all X_x
  2. jcsd
  3. Sep 22, 2013 #2


    Staff: Mentor

    One direction vector for the line is <1, 4, 6>, which I got by inspection. A normal to the plane Ax + By + Cz = D is the vector <A, B, C>. Once you know the direction of a line and a point on it, it's straightforward to get the equation of the line.
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