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Question
Find the equation of the line passing through the point (1, 2, −4) and parallel to the line \[\frac{x - 3}{4} = \frac{y - 5}{2} = \frac{z + 1}{3} .\]
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Solution
The direction ratios of the line parallel to line \[\frac{x - 3}{4} = \frac{y - 5}{2} = \frac{z + 1}{3}\] are proportional to 4, 2, 3.
Equation of the required line passing through the point (1, 2,-4) having direction ratios proportional to 4, 2, 3 is
\[\frac{x - 1}{4} = \frac{y - 2}{2} = \frac{z - \left( - 4 \right)}{3}\]
\[ = \frac{x - 1}{4} = \frac{y - 2}{2} = \frac{z + 4}{3}\]
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