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Mathematics · 2023 · 2 marks
Three Dimensional GeometryDirection Cosines and Direction Ratios of a Line2 marksApplyvery short answer
CBSE 2023 · Region 3 · Set 3 · Q23
Find the direction cosines of the line whose Cartesian equations are 5 x -3=15 y +7=3-10 z.
Find the direction cosines of the line whose Cartesian equations are $\displaystyle 5 \mathrm{x}-3=15 \mathrm{y}+7=3-10 \mathrm{z}$.
Marking-scheme solution
Equations of given line can be written as
$$\begin{aligned}
& \frac{\mathrm{x}-\dfrac{3}{5}}{\dfrac{1}{5}}=\frac{\mathrm{y}+\dfrac{7}{15}}{\dfrac{1}{15}}=\frac{\mathrm{z}-\dfrac{3}{10}}{-\dfrac{1}{10}} \\
& \text { d.r.'s are }<\frac{1}{5}, \frac{1}{15},-\frac{1}{10}>\text { or }<6,2,-3> \\
& \text { d.c.'s are }<\frac{6}{7}, \frac{2}{7},-\frac{3}{7}>
\end{aligned}
$$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.