Finding Vector Equation for a Perpendicular Line Passing Through a Point

[PsychonautQQ]

Homework Statement

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

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

 

[Mark44]

Homework Statement

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

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

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.