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

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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.