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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 6 · Set 3 · Q25
Find the angle at which the given lines are inclined to each other: l_1: (x -5)/2=(y +3)/1=(z -1)/-3; l_2: x/3=(y -1)/2=(z +5)/-1
Find the angle at which the given lines are inclined to each other : \[\begin{aligned} & l_{1}: \frac{\mathrm{x}-5}{2}=\frac{\mathrm{y}+3}{1}=\frac{\mathrm{z}-1}{-3} \\ & l_{2}: \frac{\mathrm{x}}{3}=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}+5}{-1} \end{aligned} \]
Marking-scheme solution
Let $\displaystyle \theta$ be the angle between given lines
\[\begin{aligned}
& \therefore \cos \theta=\frac{(2 \times 3)+(1 \times 2)+(-3 \times-1)}{\sqrt{14} \sqrt{14}} \\
& \Rightarrow \cos \theta=\frac{11}{14} \\
& \Rightarrow \theta=\cos ^{-1}\left(\frac{11}{14}\right)
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.