CBSE 2025 · Region 2 · Set 2 · Q24 · 2 marks

Let $\displaystyle \overrightarrow{\mathrm{p}}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{q}}=-3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$. Express $\displaystyle \overrightarrow{\mathrm{r}}$ in the form of $\displaystyle \vec{\mathrm{r}}=\lambda \vec{\mathrm{p}}+\mu \vec{\mathrm{q}}$ and hence find the values of $\displaystyle \lambda$ and $\displaystyle \mu$.

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.