Question

Find a plane that is perpendicular to the two planes x + y = 3 and x + 2y - z = 4.

Answer 1

To find a plane that is perpendicular to two given planes, we find the normal vectors of the two planes and take their cross product.

Step-by-step explanation:

To find a plane that is perpendicular to two given planes, we can find the normal vectors of the two planes and take their cross product. The cross product of two vectors will give us a vector perpendicular to both of them. Let's find the normal vectors of the given planes:

Plane 1: x + y = 3
The normal vector is (1, 1, 0)

Plane 2: x + 2y - z = 4
The normal vector is (1, 2, -1)

Now, we can take the cross product of the two normal vectors:

(1, 1, 0) x (1, 2, -1) = (-1, 1, 1)

So, the plane perpendicular to both given planes is -x + y + z = 0.