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Sketch the graph for
Also, find the intercepts and the distance of the plane from the origin.
Solution:
The given equation above represents a plane in the x, y, and z axes. To sketch the graph of a plane, let's consider the following procedure as follows
For
Set x = 0 and the equation becomes
If y = 0, then z = 2 and if z = 0, then y = 4.
Set y = 0 and the equation becomes
If x = 0, then z = 2 and if z = 0, then x = 6.
Set z = 0 and the equation becomes
If x = 0, then y = 4 and if y = 0, then x = 6.
Therefore the intercepts are:
x-intercept = 6
y-intercept = 4
z-intercept = 2
From the values of intercepts, we can plot the points in the x, y, and z axes and sketch the graph by connecting all the points as follows
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| Photo by Math Principles in Everyday Life |
The distance from a point to a plane is given by the formula
where the sign of the radical is the opposite sign of D.
In this case if the equation of a plane is
and a point is the origin, therefore the distance of a plane to the origin is
