Find the equation of the plane through the points (2, 1, 1) and (1, 3, 4) and perpendicular to the plane `x+2y+4z=10.`

Explanation

To find the equation of the plane through the points \( (2, 1, 1) \) and \( (1, 3, 4) \) that is also perpendicular to the plane given by the equation \( x + 2y + 4z = 10 \), we can follow these steps:

### Step 1: Identify the normal vector of the given plane
The equation of the plane \( x + 2y + 4z = 10 \) can be expressed in the form \( Ax + By + Cz = D \). Here, the coefficients \( A, B, C \) represent the components of the normal vector \( \vec{n_1} \) of the plane. Thus, we have:
\[ \vec{n_1} = (1, 2, 4) \]

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