Question

Equation of plane which is parallel to X - axis will be -

• A. mx + nz = C
• B. my + nz = C
• C. mx + ny = C
• D. None of these.

Answer 1

The correct option is B

my + nz = C

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 X axis -

Let r be = xi + yj + zk

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

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

To write n vector here, we have to understand couple of things.

If a plane is parallel to X - axis then we can say that its normal will always be perpendicular to X -axis.

The general equation of normal vector can be given by li + mj + nk

This vector should be in such a way that its dot product with a vector along X - axis which is “i” should be Zero.

So, (li + mj + nk). (i) = 0

Which is possible only when l = 0

So, l will be equal to zero. And the equation of normal will be mj + nk

Now we have all the information required to write the normal form of a plane.

(r - a) . n = 0

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

$m(y-a_2)+n(z-a_3)$ is a constant term. Let it be C.

So, the equation will be my + nz = C