Final answer:
To obtain the equation of a plane containing two lines, find a common point and non-collinear direction vectors from the lines, use the cross product to get the normal vector, and form the equation by plugging the point into ax + by + cz = d.
Step-by-step explanation:
To find the equation of a plane that contains two given lines, you need to establish a few things first. You need a point that lies on both lines, and the direction vectors of the lines can be used to create two non-collinear vectors that lie in the plane. Once you have a point and two directional vectors, you can use the point and the cross product of the two direction vectors to find the normal of the plane. The equation of the plane can be written as ax + by + cz = d, where (a, b, c) is the normal vector and d is calculated by plugging the coordinates of the known point into the plane equation.
Remember to verify that the vectors are not collinear and that the point does indeed lie on both lines before proceeding to calculate the normal using the cross product. After finding the normal vector, substitute a point's coordinates to determine the value of d, finalizing the equation of the plane.