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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 1 · Q10
(a) If a line makes 60° and 45° angles with the positive directions of x-axis and z-axis respectively, then find the angle that it makes with the…
(a)
If a line makes $\displaystyle 60$° and $\displaystyle 45$° angles with the positive directions of x-axis and z-axis respectively, then find the angle that it makes with the positive direction of y-axis. Hence, write the direction cosines of the line.
OR
(b)
Check whether the lines $\displaystyle \frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}-2}{3}=\frac{\mathrm{z}-3}{4}$ and $\displaystyle \frac{\mathrm{x}-4}{5}=\frac{\mathrm{y}-1}{2}=\mathrm{z}$ are skew or not.
Marking-scheme solution
(a) \(\displaystyle l=\cos 60^{\circ}=\frac{1}{2}, n=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\)
Now, \(\displaystyle l^{2}+m^{2}+n^{2}=1\)
\[\Rightarrow \frac{1}{4}+m^{2}+\frac{1}{2}=1
\]
\[\Rightarrow m^{2}=\frac{1}{4} \Rightarrow m= \pm \frac{1}{2}
\]
\[\theta=60^{\circ}
\]
Required direction cosines are \(\displaystyle \left\langle\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}\right\rangle\)All Three Dimensional Geometry questions2022 question paperNCERT solutions: Three Dimensional GeometryPractice Three Dimensional Geometry →
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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.