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qr code vb.net open source Are you confused in Visual Studio .NET
Are you confused Read ANSI/AIM Code 39 In .NET Framework Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in Visual Studio .NET applications. Encode USS Code 39 In .NET Framework Using Barcode creation for VS .NET Control to generate, create USS Code 39 image in .NET framework applications. The standardform equation of a plane in xyz space looks like an extrapolation of the standardform equation of a straight line in the xy plane This can confuse some people Don t let it baffle you! An equation of the form ax + by + cz + d = 0 where a, b, c, and d are constants represents a plane, not a line In Chap 18, you ll learn how to describe straight lines in Cartesian xyz space Code 3 Of 9 Decoder In .NET Using Barcode scanner for .NET framework Control to read, scan read, scan image in .NET framework applications. Bar Code Creator In .NET Framework Using Barcode generation for Visual Studio .NET Control to generate, create barcode image in Visual Studio .NET applications. Here s a challenge! Recognize Barcode In Visual Studio .NET Using Barcode recognizer for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications. Code 3/9 Maker In Visual C#.NET Using Barcode creation for VS .NET Control to generate, create Code 39 image in .NET applications. Draw a graph of the plane represented by the following equation: 2x 4y + 3z 12 = 0
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Bar Code Creator In VS .NET Using Barcode creator for Visual Studio .NET Control to generate, create barcode image in .NET applications. Drawing Code 39 Extended In VS .NET Using Barcode creation for Visual Studio .NET Control to generate, create Code39 image in .NET applications. Let s work out the graph by finding the coordinateaxis intercepts The xintercept, or the point where the plane intersects the x axis, can be found by setting y = 0 and z = 0, and then solving the resultant equation for x Let s call this point P We have 2x 4 0 + 3 0 12 = 0 Solving stepbystep, we get 2x 12 = 0 2x = 12 x = 12/( 2) = 6 Therefore P = ( 6,0,0) Print GS1  12 In VS .NET Using Barcode drawer for Visual Studio .NET Control to generate, create GTIN  12 image in .NET applications. Make British Royal Mail 4State Customer Code In VS .NET Using Barcode creation for Visual Studio .NET Control to generate, create RM4SCC image in VS .NET applications. Planes
EAN / UCC  13 Generation In .NET Framework Using Barcode drawer for ASP.NET Control to generate, create GS1 128 image in ASP.NET applications. Code128 Maker In None Using Barcode printer for Software Control to generate, create Code 128A image in Software applications. The yintercept, or the point where the plane intersects the y axis, can be found by setting x = 0 and z = 0, and then solving the resultant equation for y Let s call this point Q We have 2 0 4y + 3 0 12 = 0 Solving, we get 4y 12 = 0 4y = 12 y = 12/( 4) = 3 Therefore Q = (0, 3,0) The zintercept, or the point where the plane intersects the z axis, can be found by setting x = 0 and y = 0, and then solving the resultant equation for z Let s call this point R We have 2 0 4 0 + 3z 12 = 0 Solving, we get 3z 12 = 0 3z = 12 z = 12/3 = 4 Therefore R = (0,0,4) These three points are shown in Fig 172 We can now envision the plane because, as we recall from our courses in spatial geometry, a plane in three dimensions can be uniquely defined on the basis of three points GTIN  128 Printer In None Using Barcode drawer for Word Control to generate, create USS128 image in Word applications. Paint Data Matrix 2d Barcode In ObjectiveC Using Barcode encoder for iPhone Control to generate, create Data Matrix image in iPhone applications. +y P = ( 6, 0, 0) Each axis division is 1 unit
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Figure 172 Here s the graph of a plane, based on the locations of the three axis intercept points P, Q, and R
Surfaces in ThreeSpace
Spheres
A spherical surface is defined as the set of all points that lie at a fixed distance from a known central point in three dimensions When we recall the formula for the distance between a point and the origin, it s easy to work out equations for spheres in Cartesian xyz space Center at the origin Imagine a sphere whose center lies at the origin (0,0,0), as shown in Fig 173 Any point on the sphere s surface is at the same distance from the origin as any other point on the sphere s surface Suppose that P is one such point whose coordinates are given by P = (xp,yp,zp) In Chap 7, we learned that the distance r of the point P from the origin in Cartesian xyz space is r = (xp2 + yp2 + zp2)1/2 We can square both sides of the above equation to get r2 = xp2 + yp2 + zp2 +y Center of sphere is at (0, 0, 0) Radius = r
Figure 173 A sphere of radius r in Cartesian xyz space, centered at the origin All points on the sphere s surface are at distance r from the center point (0,0,0) Spheres
Transposing the left and righthand sides, we have xp2 + yp2 + zp2 = r2 Every point on the sphere s surface is the same distance from the origin as P, so we can generalize the above equation to get x2 + y2 + z2 = r2 which defines the set of all points in three dimensions that lie at a fixed distance r from the origin That s all there is to it! We ve found the standardform equation for a sphere of radius r, centered at the origin in Cartesian xyz space Center away from the origin Consider a sphere whose center is somewhere other than the origin in Cartesian xyz space Suppose that the coordinates of the center point are (x0,y0,z0), as shown in Fig 174 Whatever point P that we choose on the sphere s surface, the distance between P and the center is equal to the sphere s radius r Adapting the distancebetweenpoints formula for Cartesian xyz space from Chap 7, we get r = [(xp x0)2 + (yp y0)2 + (zp z0)2]1/2 Center of sphere is at (x0, y0, z0)

