Your problem is thinking of <8, 4, 8> as the "direction vector" for the plane. A line has a direction vector that points in the direction of the line. A plane has a normal vector. <8, 4, 8> points perpendicular to the plane.
The question reads
"For what values of a and b is the line L othogonal to the plane 8x+4y+8z=14"
Line L is given in parametric equations.
x=15+2t
y=8+at
z=4+bt
If someone could give me pointers on how to start this problem is would be great!
So far, I know:
Direction vector for the plane is <8,4,8>
Direction vector for the line is <2,a,b>
So is the direction vector for the line <2,1,2>?
Since <8,4,8> would be 4<2,a,b>.
Correct?
Or is this a line parallel to the plane? Sorry if this is a dumb question.
Your problem is thinking of <8, 4, 8> as the "direction vector" for the plane. A line has a direction vector that points in the direction of the line. A plane has a normal vector. <8, 4, 8> points perpendicular to the plane.