I have the equation a given plane in the format: $$ax+by+cz+d=0$$ And I have a line in the following format: $$<a,b,c>+t<d,e,f>$$ I have the normal vector that identifies the plane: $$\vec{n}=<a,b,c>$$ I have the vector parallel to the line: $$\vec{v}=<d,e,f>$$ I then take the dot product of the two vectors and get the a non-zero number: $$\vec{n} \ \cdot \ \vec{v} \ne0$$
From here i can deduce that the plane, and the line are not parallel; however, how do I know if they are not perpendicular?
One observation I have the make is that: $$\vec{n} = k\vec{v}$$ So since they are scalar multiples of each other are they perpendicular?