Find the equations of a line which is parallel to the line $fraction numerator straight x minus 2 over denominator 3 end fraction space equals fraction numerator straight y plus 1 over denominator 1 end fraction space equals space fraction numerator straight z minus 7 over denominator 9 end fraction$ and which passes through the point (3, 0, 5).

Solution

Direction-ratios of the line

fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator 1 end fraction space equals fraction numerator straight z minus 7 over denominator 9 end fraction space space are space 3 comma space 1 comma space 9

∴ equations of line through (3, 0, 5) and having direction-ratios 3, 1, 9 are

fraction numerator straight x minus 3 over denominator 3 end fraction space equals space fraction numerator straight y minus 0 over denominator 1 end fraction space equals space fraction numerator straight z minus 5 over denominator 9 end fraction

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