Find the distance between the planes r .(2i - 3j +6k) - 4 = 0 and… - Vidyadip

Question

Find the distance between the planes $\overrightarrow{\text{r}}.(2\hat{i} - 3\hat{j} +6\hat{k}) - 4 = 0 \text{ and}\overrightarrow{\text{r}}.(6\hat{i} - 9\hat{j} +18\hat{k}) + 30 = 0.$

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Answer

Writing or using, that given planes are parallel
$d = \frac{|\ 4 + 10\ |}{\sqrt{\ 4\ +\ 9 \ + \ 36}} = 2 \text{ units}$

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