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.

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- February 7th 2013, 02:48 PMGiestforlifeFinding if a line intersects the plane or not
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. - February 7th 2013, 03:04 PMPlatoRe: Finding if a line intersects the plane or not
- February 7th 2013, 06:30 PMGiestforlifeRe: Finding if a line intersects the plane or not
- February 7th 2013, 07:07 PMSorobanRe: Finding if a line intersects the plane or not
Hello, Giestforlife

Quote:

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 doesintersect the plane.*not*

. . 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.