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Question
If the equations of a line AB are
\[\frac{3 - x}{1} = \frac{y + 2}{- 2} = \frac{z - 5}{4},\] write the direction ratios of a line parallel to AB.
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Solution
We have
\[\frac{3 - x}{1} = \frac{y + 2}{- 2} = \frac{z - 5}{4},\]
The equation of the line AB can be re-written as
\[\frac{x - 3}{- 1} = \frac{y + 2}{- 2} = \frac{z - 5}{4}\]
Thus, the direction ratios of the line parallel to AB are proportional to -1 , - 2 , 4 .
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