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To decide if the lines are coincident, we check to see whether a point on one of the lines satisfies the vector equation of the other. The point (- 3, 1, 4) is on the second line. If it is also on the first line, then (- 3, 1, 4) = (4, 4, 1) + t(3, - 4, - 1).
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Then - 3 = 4 + 3t                1 = 4 - 4t                4 = 1 - t

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            3t = - 7                     4t = 3                     t = - 3

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           t = - 7/3                     t = 3/4                     t = - 3

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Since the parameter value t is different obtained each equation, the point (- 3, 1, 4) from the second line does not lie on the first line, and the lines are distinct.

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The two line are not parallel and these are distinct. So, the two lines are not same.

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