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?

1 Answer
Jan 28, 2018

See explanation.


The direction vector of the line is #[2,1,3]#. That vector is parallel to the line.

The normal vector to the plane is #[2, -1, -1]#. That vector, as the name implies, is normal to the plane.

Calculating the dot product of the two vectors gives:

#[2,1,3] cdot [2, -1, -1] = 4-1-3=0#

Since the dot product is 0 we know the vectors are orthogonal.

Since both the plane and the line are orthogonal to the vector #[2, -1, -1]# they are parallel to each other.