Solution
The vector (3, 4, -2) is normal or perpendicular to the plane 3x + 4y - 2z = 1.
Also, (-2, 5, 7) is the direction vector for the given line.
If this line is parallel to the plane then its direction vector must be perpendicular to the plane's normal vector.
If two vectors are perpendicular then their scalar or dot product is zero.
All we have to do is to work out (3, 4, -2).(-2, 5, 7).
Doing this gives -6 + 20 - 14 = 0 so therefore this line is parallel to this plane.

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