Question

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

Answer 1

To find the equation of the plane that passes through a given point and contains a line of intersection of two planes, we can use the cross product of the normal vectors of the planes and the given point.

Step-by-step explanation:

To find the equation of the plane that passes through the point (1, 2, 1) and contains the line of intersection of the planes x + 2y + 3z = 1 and 2x - y + z = -3, we can use the following steps:

1. Find the direction vector of the line of intersection by taking the cross product of the normal vectors of the two planes.
2. Use the given point and the direction vector to write the vector equation of the line.
3. Find the equation of the plane by substituting the coordinates of the given point and the direction vector into the equation of a plane.

The equation of the plane is obtained by simplifying the expression from step 3.