Question

Find the cartesian equation of the line which passes through the point (-2, 4, -5) and is parallel to the line given by $fraction numerator straight x plus 3 over denominator 3 end fraction space equals space fraction numerator straight y minus 4 over denominator 5 end fraction space equals fraction numerator straight z plus 8 over denominator 6 end fraction$

Solution

Direction-ratios of the line $fraction numerator straight x plus 3 over denominator 3 end fraction space equals fraction numerator straight y minus 4 over denominator 5 end fraction space equals fraction numerator straight z plus 8 over denominator 6 end fraction space space are space 3 comma space 5 comma space 6.$
∴ equation of the line through (–2, 4, –5) and having direction ratios 3, 5, 6 are
$fraction numerator straight x plus 2 over denominator 3 end fraction space equals fraction numerator straight y minus 4 over denominator 5 end fraction space equals fraction numerator straight z plus 8 over denominator 6 end fraction$

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Three Dimensional Geometry

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