Question

Which of the following is not the correct formula for representing a plane?

(a) \(\vec{r}.\hat{n}=d\)

(b) ax+by+cz=d

(c) lx+my+nz=d

(d) al+mb+cn=d^2

The question was asked in examination.

Asked question is from Three Dimensional Geometry topic in chapter Three Dimensional Geometry of Mathematics – Class 12

Answer 1

The correct option is (d) al+mb+cn=d^2

For explanation I would say: \(\vec{r}.\hat{n}=d\), ax+by+cz=d, lx+my+nz=d are the various ways of representing a plane.

\(\vec{r}.\hat{n}\)=d is the vector equation of the plane, where \(\hat{n}\) is the unit vector normal to the plane.

ax+by+cz=d, lx+my+nz=d are the Cartesian equation of the plane in the normal form where, a, b, c are the direction ratios and l, m, n are the direction cosines of the normal to the plane respectively.