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 .
Are they perpendicular or parallel?
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.