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Q.
The distance of the plane $\vec{r} \cdot (3 \hat{i} + 4 \hat{j} + 12 \hat{k} ) = 65$ from the origin is
Introduction to Three Dimensional Geometry
Solution:
The given equation is $\vec{r} . (3 \hat{i} + 4 \hat{j} + 12 \hat{k}) = 65$
or $\vec{r} . \left( \frac{3}{13} \hat{i} + \frac{4}{13} \hat{j} + \frac{12}{13} \hat{k} \right) = 5$ ,
which is of the form $\vec{r} . \hat{n} = p $