Question

Equation of plane which is parallel to XY-plane is

• A. x = a ; where a is constant.
• B. y = b ; where b is constant.
• C. z = c ; where c is constant.
• D. (x - a) + (y - b) = c ; where a, b,and c are constants.

Answer 1

The correct option is C

z = c ; where c is constant.

Let’s write the normal form of the plane.

(r - a) . n = 0

Where r is a general vector in that plane and a is fixed vector. So (r - a) will be the vector lying in that plane. And n vector is the normal vector to that plane.

For a plane parallel to XY plane -

Let r = xi + yj + zk

And $a=a_{1}i+a_{2}j+a_{3}k$

$So(r-a)=(x-a_1)i+(y-a_2)j+(z-a_3)k$

Here n will be = ck (As the normal to a plane which is parallel XY plane will be along Z- axis.)

Thus the equation of plane will be -

$\left(\right(x-a_1)i+(y-a_2)j+(z-a_3\left)k\right).\left(ck\right)=0$

$Or(z-a_3).c=0$

$Orz=a_3$

On comparing it with the given options we can say “C” is correct.