Solve this following

Question:

i. If $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$, show that $(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}})$ is perpendicular to $(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}})$.

ii. If $\overrightarrow{\mathrm{a}}=(5 \hat{\mathrm{i}}-\hat{\mathrm{j}}-3 \hat{\mathrm{k}})$ and $\overrightarrow{\mathrm{b}}=(\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-5 \hat{\mathrm{k}})$ then show that $(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}})$ and $(\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}})$ are orthogonal.

Solution: