Posted by **Gabe** on Sunday, May 30, 2010 at 5:43pm.

Determine the caresian equaiton of a plane that pass through point P(1,2,2) and is perpendicular to the line (x,y,z)= 3,-1,-4 + t(-2,3,1)

- Vector -
**MathMate**, Sunday, May 30, 2010 at 5:58pm
If the plane is perpendicular to

L: (3,-1,-4)+t(-2,3,1)

in which the vector (-2,3,1) is parallel to the line, and therefore perpendicular to the plane P, then

the required plane is:

-2x+3y+z+k=0

where k is a constant to be determined.

Since the required plan passes through P(1,2,2), we substitute P in the plane to get:

-2(1)+3(2)+(2)+k=0

or k=-6

Therefore the plane is given by:

-2x+3y+z-6=0

Check by joining any two distinct points on the plane to form a vector and prove that the vector is perpendicular to line L.

## Answer this Question

## Related Questions

- algebra - the line "l" passes through the point P=(1,-1,1) and has a direction ...
- Vectors - Determine the vector equation of a line passing through the point P(3,...
- Three Dimensions/Calculus - Find the general form of the equation of the plane ...
- math - A vector equation for a given straight line is r = (i + 3j) + lambda (-i...
- calculus - find a vector equation of the line, which passes through the point (...
- Analytic Geometry/Calculus - We didn't go over the perpendicular form in class, ...
- Precalc - At the point were a line intersects a plane [with the equation (24x+...
- Math - a line RS is perpendicular to plane p at R. If T is a second point not on...
- Geometry - a line RS is perpendicular to plane p at R. If T is a second point ...
- Vector - 2. Determine the Cartesian equation of the plane passing through the ...