If the line x = 1-4t; y = 3; z = 2t +2 intersects the plane x + 2y +2z = 5?
I already tried plugging in the parametrization of the line into the equation of the plane, but I get an indeterminate answer!
Any help is greatly appreciated.
Hello, Giestforlife
I tried plugging in the parametrization of the line into the equation of the plane,
. . but I get an indeterminate answer!
Not sure what you mean by "indeterminate".
We have: .
and we get: . . . . a false statement.
This means that the line does not intersect the plane.
. . They are parallel.
We can check this fact.
The direction vector of the line is:.
The normal vector of the plane is:.
And:.
The line and the normal vector are perpendicular.
Therefore, the line and plane are parallel.