Question

Find an equation of he plane that passes through the point (4, 3, 2) and contains the line of intersection of the planes x + 2y + 3z = 1 and 2x − y + z = −3

Answer 1

To find an equation of the plane that passes through a point and contains the line of intersection of two given planes, we can find the direction vector of the line by taking the cross product of the normal vectors of the planes. Then, substitute the coordinates of the point and the direction vector into the equation of a plane to find the equation.

Step-by-step explanation:

To find an equation of the plane that passes through the point (4, 3, 2) and contains the line of intersection of the planes x + 2y + 3z = 1 and 2x − y + z = −3, we can first find the direction vector of the line of intersection by taking the cross product of the normal vectors of the two planes.

1. Find the normal vectors of the two given planes.
2. Take the cross product of the normal vectors to find the direction vector of the line of intersection.
3. Substitute the coordinates of the point and the direction vector into the equation of a plane to find the equation of the plane.

The equation of the plane is Ax + By + Cz = D, where A, B, C are the components of the direction vector and D can be found by substituting the coordinates of the point into the equation.