CBSE 2023 · Region 4 · Set 2 · Q20 · 1 mark

Assertion ( $\displaystyle A$ ) : The lines $\displaystyle \overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}_{1}}+\lambda \overrightarrow{\mathrm{b}_{1}}$ and $\displaystyle \overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}_{2}}+\mu \overrightarrow{\mathrm{b}_{2}}$ are perpendicular, when $\displaystyle \overrightarrow{\mathrm{b}_{1}} \cdot \overrightarrow{\mathrm{b}_{2}}=0$. Reason $\displaystyle (R)$ : The angle $\displaystyle \theta$ between the lines $\displaystyle \overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}_{1}}+\lambda \overrightarrow{\mathrm{b}_{1}}$ and \[\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}_{2}}+\mu \overrightarrow{\mathrm{b}_{2}} \text { is given by } \cos \theta=\frac{\overrightarrow{\mathrm{b}_{1}} \cdot \overrightarrow{\mathrm{~b}_{2}}}{\left|\overrightarrow{\mathrm{~b}_{1}}\right|\left|\overrightarrow{\mathrm{b}_{2}}\right|} \]

CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.