6. Find out if the line r = (1, 3, 8) + t (-2, 5, 7) is parallel to the plane 3x + 4y - 2z = 1

Answer 1

Take a vector that lies on the line (-2,5,7).
Check if this vector is perpendicular to the normal vector of the plane (3,4,-2).

If the dot product between them is zero, the two vectors are perpendicular, and therefore the line is parallel to the plane.