Assertion ( A ): The lines r = a_1 +λ b_1 and r = a_2 +μ b_2 are perpendicular, when b_1 · b_2 =0. Reason (R): The angle θ between the lines r = a_1…

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 \[\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}_{2}}+\mu \overrightarrow{\mathrm{b}_{2}} \text { is given by } \cos \theta=\frac{\overrightarrow{\mathrm{b}_{1}} \cdot \overrightarrow{\mathrm{~b}_{2}}}{\left|\overrightarrow{\mathrm{~b}_{1}}\right|\left|\overrightarrow{\mathrm{b}_{2}}\right|} \]