Question

Equation of plane passing through a point A given by position vector $\overline{a}$ and perpendicular to $\hat{n}is(\overline{r}-\overline{a}).\hat{n}=0$ .

• A. True
• B. False

Answer 1

The correct option is A

True

Here our aim is to find an equation, simply put the locus of all points which form the given plane. You can approach this by imagining all planes which are perpendicular to $\hat{n}$. Clearly there are $\infty$ such planes. But we have an extra condition which restricts the number to 1. Moreover if is a general vector which gives the position of the point we can see that $(\overline{r}-\overline{a}).\hat{n}=0as(\overline{r}-\overline{a})$ lies on the plane and $\hat{n}$ is perpendicular to the given plane. Hence $(\overline{r}-\overline{a}).\hat{n}=0$ serves as an expression for a plane. So the given statement is true.