Mathematics

The equation $\tilde{r} \cdot (2\tilde{i} + \tilde{j} + 2\tilde{k}) = 5$ describes a plane, and the vector multiplying $\tilde{r}$ is its normal vector—it points straight out of the plane. To find the unit normal, you just need to normalize this normal vector by dividing it by its own magnitude. This is a direct application of the plane equation's geometry.

The equation $\tilde{r} \cdot (2\tilde{i} + \tilde{j} + 2\tilde{k}) = 5$ describes a plane, and the vector multiplying $\tilde{r}$ is its normal vector—it points straight out of the plane. To find the unit normal, you just need to normalize this normal vector by dividing it by its own magnitude. This is a direct application of the plane equation's geometry.