# Show that the following planes are at right angles:

Question:

Show that the following planes are at right angles:

(i) $\overrightarrow{\mathrm{r}} \cdot(4 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-8 \hat{\mathrm{k}})=5$ and $\overrightarrow{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})+10=0$

(ii) $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+6 \hat{\mathrm{k}})=13$ and $\overrightarrow{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-5 \hat{\mathrm{k}})+7=0$

Solution: