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Mathematics · 2022 · 2 marks
Three Dimensional GeometryDirection Cosines and Direction Ratios of a Line2 marksRemembervery short answer
CBSE 2022 · Region 5 · Set 3 · Q1
The Cartesian equation of a line A B is: (2 x-1)/12=(y+2)/2=(z-3)/3 Find the direction cosines of a line parallel to line AB.
The Cartesian equation of a line $\displaystyle A B$ is : \[\frac{2 x-1}{12}=\frac{y+2}{2}=\frac{z-3}{3} \] Find the direction cosines of a line parallel to line AB .
Marking-scheme solution
Equation of line
\[\frac{x-\dfrac{1}{2}}{\dfrac{12}{2}}=\frac{y+2}{2}=\frac{z-3}{3}
\]
Direction ratios of line are $\displaystyle 6$, $\displaystyle 2$, $\displaystyle 3$
Direction cosines of line are \(\displaystyle \left\langle\frac{6}{7}, \frac{2}{7}, \frac{3}{7}\right\rangle\)
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.