Question

Which of the following is the general equation of plane ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Equation of a plane with a non zero normal vector n = (a, b, c) through the point

$M=(x_0,y_0,z_0)isn.(OL-OM)=0whereL=(x,y,z)$ and "O" is origin.

$(aj+bj+ck).\left(\right(xi+yj+zk)-(x_{0}i+y_{0}j+z_{0}k\left)\right)=0$

$(aj+bj+ck).(x-x_0)i+(y-y_0)j+(z-z_0)k)=0$

Which gives the general equation of a plane.

ax+ by+ cz+ d = 0,

Where $d=-a{x}_0-b{y}_0-c{z}_0$

From here we can see that equation of a plane is a first order equation which matches with only one option given.