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+z6=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 (1...
 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 ...
More Related Questions