Question

The line l passes through the point P = (1,-1,1) and has direction vector d = [2,3,1]. Determine whether l and the plane 4x-y+5z = 0 are parallel, perpendicular, or neither.

Answer 1

Hello : 
the normal vector of the plane is : d' = [4,-1,5]...(vector  perpendicular to the plane)
d ⊥ d' because : (4)(2)+(-1)(3)+(5)(1)=0
the line is perpendicular to the plane .