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Question
Write the direction cosines of the line \[\frac{x - 2}{2} = \frac{2y - 5}{- 3}, z = 2 .\]
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Solution
We have
\[\frac{x - 2}{2} = \frac{2y - 5}{- 3}, z = 2\]
The equation of the given line can be re-written as
\[\frac{x - 2}{2} = \frac{y - \frac{5}{2}}{- \frac{3}{2}} = \frac{z - 2}{0}\]
\[ \Rightarrow \frac{x - 2}{4} = \frac{y - \frac{5}{2}}{- 3} = \frac{z - 2}{0}\]
The direction ratios of the given line are proportional to 4,-3,0.
Hence, the direction cosines of the given line are proportional to
\[\frac{4}{\sqrt{4^2 + \left( - 3 \right)^2 + 0^2}}, \frac{- 3}{\sqrt{4^2 + \left( - 3 \right)^2 + 0^2}}, \frac{0}{\sqrt{4^2 + \left( - 3 \right)^2 + 0^2}}\]
\[ = \frac{4}{5}, \frac{- 3}{5}, 0\]
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