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