Find the cartesian equation of the plane which passes through the point
(3,-4, 1) and which is parrallel to the plane containing the point (1,2,-1) and the line r=t( i+j+k)
Hello, kingkaisai2!
Find the equation of the plane which passes through the point and which is
parallel to the plane containing the point and the line
To write the equation of a plane, we need a point and its normal direction:
. . Then the equation is: .
We have a point , so we need the normal vector:
Since this plane is parallel to the plane containing point and line ,
. . it has the same normal vector.
The line has parametric equations: .
For , we have the point:
For , we have the point:
Hence, the plane contains points:
The normal vector is perpendicular to and
Since and
. .
So the desired plane has point and normal
Can you finish it now?