CBSE 2025 · Region 6 · Set 1 · Q25 · 2 marks
Determine if the lines $\displaystyle \vec{\mathrm{r}}=(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}-\hat{\mathrm{j}})$ and $\displaystyle \overrightarrow{\mathrm{r}}=(4 \hat{\mathrm{i}}-\hat{\mathrm{k}})+\mu(2 \hat{\mathrm{i}}+3 \hat{\mathrm{k}})$ intersect with each other.
Marking-scheme solution
\[\begin{aligned}
& \vec{b}_{1}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}, \vec{b}_{2}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{a}_{2}}=4 \hat{\mathrm{i}}-\hat{\mathrm{k}}, \vec{\mathrm{a}}_{1}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}} \\
& \left(\overrightarrow{\mathrm{a}_{2}}-\vec{\mathrm{a}}_{1}\right)=3 \hat{\mathrm{i}}-\hat{\mathrm{j}} \\
& \vec{b}_{1} \times \vec{b}_{2}=-3 \hat{\mathrm{i}}-9 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}
\end{aligned}
\]
Three Dimensional GeometryShortest Distance between Two LinesAnalysevery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.