Question:
Find the value of $\lambda$ for which the given planes are perpendicular to each other:
(i) $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\lambda \hat{\mathrm{k}})=7$ and $\overrightarrow{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})=9$
(ii) $\overrightarrow{\mathrm{r}} \cdot(\lambda \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})=5$ and $\overrightarrow{\mathrm{r}} \cdot(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-7 \hat{\mathrm{k}})+11=0$
Solution:
