Question

Find the direction numbers for the line of intersection of the planes x + y + z = 5 and x + z = 0.

Answer 1

The direction numbers for the line of intersection are -1, 2, -1.

Step-by-step explanation:

To find the direction numbers for the line of intersection of the planes x + y + z = 5 and x + z = 0, we need to find the normal vectors of the planes. The normal vector for the first plane is (1, 1, 1), and the normal vector for the second plane is (1, 0, 1). The direction numbers of the line of intersection can be obtained by taking the cross product of these two normal vectors. Performing the cross product, we get (-1, 2, -1). Therefore, the direction numbers for the line of intersection are -1, 2, -1.