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)

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- Oct 28th 2006, 12:24 AMkingkaisai2Vector-help!
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) - Oct 28th 2006, 06:51 AMSoroban
Hello, kingkaisai2!

Quote:

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?