Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.
Solution and Explanation
The equation of the plane ZOX is y=0
Any plane parallel to it is of the form, y=a
Since, the y-intercept of the plane is 3,
∴ a=3
Thus, the equation of the required plane is y=3.
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Concepts Used:
Plane
A surface comprising all the straight lines that join any two points lying on it is called a plane in geometry. A plane is defined through any of the following uniquely:
- Using three non-collinear points
- Using a point and a line not on that line
- Using two distinct intersecting lines
- Using two separate parallel lines
Properties of a Plane:
- In a three-dimensional space, if there are two different planes than they are either parallel to each other or intersecting in a line.
- A line could be parallel to a plane, intersects the plane at a single point or is existing in the plane.
- If there are two different lines that are perpendicular to the same plane then they must be parallel to each other.
- If there are two separate planes which are perpendicular to the same line then they must be parallel to each other.