Find an equation of the plane with the given characteristics. The plane passes through the points (4, 3, 1) and (4, 1, -7) and is perpendicular to the plane 8x 7y 4z

Step-by-step explanation:

Given

Perpendicular to

Required

Determine the plane equation

The general equation of a plane is:

For

First, we need to determine parallel vector

is parallel to the required plane

From the question, the required plane is perpendicular to

Next, we determine vector

This implies that the required plane is parallel to

Hence: and are parallel.

So, we can calculate the cross product

The product is always of the form + - +

So:

Calculate the product

So, the resulting vector, n is:

Recall that:

By comparison:

Substitute these values in

Recall that:

So, we have:

Collect Like Terms

Divide through by -16

Hence, the equation of the plane is

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step-by-step explanation: