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

Category: QuestionsWhich of the following is not the correct formula for representing a plane?
Editor">Editor Staff asked 11 months ago

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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1 Answers
Editor">Editor Staff answered 11 months ago

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.