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प्रश्न
Find the Cartesian equations of the line which passes through the point (−2, 4 , −5) and is parallel to the line \[\frac{x + 3}{3} = \frac{4 - y}{5} = \frac{z + 8}{6} .\]
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उत्तर
The equation of the given line is
\[\frac{x + 3}{3} = \frac{4 - y}{5} = \frac{z + 8}{6} .\]
It can be re-written as
\[\frac{x + 3}{3} = \frac{y - 4}{- 5} = \frac{z + 8}{6}\]
Since the required line is parallel to the given line, the direction ratios of the required line are proportional to 3, -5 , 6 .
Hence, the cartesian equations of the line passing through the point ( -2, 4 , -5) and parallel to a vector having direction ratios proportional to 3 ,-5,6 is
\[\frac{x + 2}{3} = \frac{y - 4}{- 5} = \frac{z + 5}{6}\]
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