Question

In $\overline{r}.\overline{n}=d,|d|$ represents the distance between

• A. Origin and any point on the plane
• B. Points where the plane intersects the axis
• C. Foot of perpendicular along $\hat{n}$ and origin
• D. None of these

Answer 1

The correct option is C Foot of perpendicular along $\hat{n}$ and origin

Imagine a general point on the plane. Now lets see what $|\overline{r}.\hat{n}|$ represents. $|\overline{r}.\hat{n}|=|rcos\theta .1|$ $=|rcos\theta |$ Which is the projection of $\overline{r}$ and $\hat{n}$ As $\hat{n}$ is perpendicular to the plane $\overline{r}.\hat{n},|rcos\theta |$ will be distance between origin and plane. This can also be interpreted as Foot of perpendicular along $\hat{n}$ and origin. Therefore option c is correct. The distance from any point on the plane to the origin is $|\overline{r}|$. Therefore option a is wrong. Option b does not give any information about |d|. So option c is the only correct answer.