Does for every t?
If so the line is in the plane.
Give x=3-t, y=2+t, z=1-3t
a) determine whether the line and plane are parallel, perpendicular , or either.
My answer to part a) is : the line is parallel to the given plane.
b) Does the line contain in the plane?
How should I answer this part?
Thank you very much.
(a) Determine whether the line and plane are parallel, perpendicular, or neither.
My answer to part (a) is: the line is parallel to the given plane . . . yes
(b) Is the line contained in the plane?
(a) The line has direction vector:
The plane has normal vector:
If the line and plane are perpendicular, then for some nonzero number
. . This is not true . . . they are not perpendicular.
If the line and plane are parallel, then:
. . Since . . . they are parallel.
(b) The equation of the plane is: . . . . . .
Substitute the parametric equations: .
If this statement is always true, the line lies in the plane.
We get: .
. . Hence, the line does not lie in the plane.