TITLE: Solution to Problem4
# !b1 Problem4:
Show that the line
!c0 (x-1)/3 = -y/2 = z+1
and the plane x + 2y + z = 1 are parallel.
!b3 SOLUTION:
The position vector u, velocity vector v for the line are:
> u := [1,0,-1]: v := [3,-2,1]:
# A normal to the plane is:
> n := [1,2,1]:
# We have,
> dotprod(v,n);
0
# so the line is either parallel to the plane or the line is
contained in the plane. But u doesn't belong to the plane
so we are done.
>