The line l has equation r=(1 2 -1) + lamda(2 1 3). The plane has equation r.(2 -1 -1)=6 (i) show that l is parallel to p Can someone please solve this question?
The direction vector of the line is
The normal vector to the plane is
Calculating the dot product of the two vectors gives:
Since the dot product is 0 we know the vectors are orthogonal.
Since both the plane and the line are orthogonal to the vector