The value of λ for which the angle between the lines r = i + j + k +p(2 i + j +2 k ) and r =(1+ q ) i +(1+ q λ) j +(1+ q ) k is (π)/2 is:

The value of $\displaystyle \lambda$ for which the angle between the lines $\displaystyle \vec{\mathrm{r}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}+p(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}})$ and $\displaystyle \overrightarrow{\mathrm{r}}=(1+\mathrm{q}) \hat{\mathrm{i}}+(1+\mathrm{q} \lambda) \hat{\mathrm{j}}+(1+\mathrm{q}) \hat{\mathrm{k}}$ is $\displaystyle \frac{\pi}{2}$ is :