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find an equation of the plane. the plane through the point (1, −2, −8) and parallel to the plane 8x − y − z = 4

User Suanmeiguo
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Final answer:

The equation of the plane passing through the point (1, -2, -8) and parallel to the plane 8x - y - z = 4 is 8x - y - z = 2.

Step-by-step explanation:

To find an equation of the plane that passes through the point (1, −2, −8) and is parallel to the plane 8x − y − z = 4, we can use the fact that parallel planes have identical normal vectors.

Since the normal vector for the given plane is (8, −1, −1), our desired plane will have the same normal vector. The general equation of a plane is given by Ax + By + Cz = D, where (A, B, C) is the normal vector and D is a constant that can be determined by plugging in the coordinates of the given point.

Substituting the given point into the general equation we get:

8(1) − (−2) − (−8) = D

Which simplifies to 8 + 2 − 8 = D, so D = 2.

Therefore, the equation of the plane is 8x − y − z = 2.

User RakeshNS
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