Question

Equation of plane parallel to Z-axis

Answer 1

Hint: A plane is a two dimensional flat surface with zero thickness. General equation of plane is given by
$ax+by+cz+d=0$
Where a, b, c is the direction ratio of the normal to the plane. So, in order to find out the equation of the plane we have to find out the direction ratio of the plane. Once we get the direction ratio of the required plane, we will substitute the direction ratio in the standard equation of the plane we get the desired answer of the given question.in this question we have to find out the direction ratio of the plane which is parallel to the Z-axis.

Complete step-by-step answer:
Any line in x-y plane, which can be written as $ax+by+c=0$ would be perpendicular to $z-axis.$
So, the direction ratio of the plane is (a, b, 0) lying in the x-y plane.
so, equation of plane can be found if we put c = 0 in the general equation of plane
$ax+by+cz+d=0$
So, equation of plane parallel to Z-axis can be written as
$ax+by+d=0$

Note: The normal of a plane parallel to the z-axis must be perpendicular to unit vector k so that k-component of normal vector is zero. We can also find the above result by using vector properties. That is Dot product of normal and the equation of plane is zero.
If a, b, and c are three numbers proportional to the direction cosine l, m and n of a straight line then a, b and c are called direction ratio. They are also called direction numbers or direction components. Direction cosine of a line is unique but the direction ratio of a line is not unique but can be infinite as it is proportional to direction cosine.