# qr code vb.net open source What information do we need to determine the equation of a plane in Cartesian xyz space in .NET Paint Code-39 in .NET What information do we need to determine the equation of a plane in Cartesian xyz space

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Question 17-1
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What information do we need to determine the equation of a plane in Cartesian xyz space
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We can find an equation for a plane in Cartesian xyz space if we know the direction of at least one vector that s perpendicular to the plane, and if we know the coordinates of at least one point in the plane We don t have to know the magnitude of the vector, but only its direction The point s coordinates don t have to tell us where the vector begins or ends; the point can be anywhere in the plane
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Imagine a plane that passes through a point whose coordinates are (x0,y0,z0) in Cartesian xyz space Also suppose that we ve found a vector ai + bj + ck that s normal (perpendicular) to the plane Based on this information, how can we write down an equation that represents the plane
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We can write the plane s equation in the standard form a(x x0) + b(y y0) + c(z z0) = 0 We can also write the equation as ax + by + cz + d = 0 where d is a constant that works out to d = ax0 by0 cz0
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What s the general equation for a sphere centered at the origin and having radius r in Cartesian xyz space
The equation can be written in the standard form x2 + y2 + z2 = r2
Question 17-4
What s the general equation for a sphere of radius r in Cartesian xyz space, centered at a point whose coordinates are (x0,y0,z0)
The equation can be written in the standard form (x x0)2 + (y y0)2 + (z z0)2 = r2
Question 17-5
Can a sphere have a negative radius in Cartesian xyz space
Normally, we define a sphere s radius as a positive real number Nevertheless, spheres with negative radii can exist in theory If we encounter a sphere whose radius happens to be defined