Question

Find an equation of the plane. The plane through the point (3, −1, −6) and parallel to the plane 8x − y − z = 3

Answer 1

To find an equation of the plane parallel to a given plane and passing through a point, take the coefficients of the variables in the given plane equation as the components of the normal vector. Then, use the point and the normal vector to form the equation of the desired plane.

Step-by-step explanation:

To find an equation of the plane, we need a point on the plane and the normal vector of the plane. We are given the point (3, -1, -6) and that the plane is parallel to the plane 8x - y - z = 3. The coefficients of x, y, and z in the equation of the given plane are the components of the normal vector. So, the normal vector is (8, -1, -1). The equation of the desired plane is therefore 8(x-3)-(y+1)-(z+6) = 0, which can be simplified to 8x - y - z = 25.