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qr code vb.net open source Figure A6 Illustration for the solution to in Visual Studio .NET
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Code 3/9 Reader In C# Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. Printing GTIN  13 In ObjectiveC Using Barcode creator for iPad Control to generate, create EAN 13 image in iPad applications. 1 In Fig 77, the x axis goes from left to right, the y axis goes from bottom to top, and the z axis goes from far to near According to the following rules: The origin has x = 0, y = 0, and z = 0 The point P has x = 3, y = 3, and z = 4 The point Q has x = 5, y = 4, and z = 0 The point R has x = 0, y = 0, and z = 6 2 We have P = (3, 3,4) Let s call the coordinates xp = 3, yp = 3, and zp = 4 When we plug these values into the formula for the distance c of a point from the origin, we get c = (xp2 + yp2 + zp2)1/2 = [32 + ( 3)2 + 42]1/2 = (9 + 9 + 16)1/2 = 341/2 502 WorkedOut Solutions to Exercises: 19 That s an irrational number When we use a calculator to approximate its value to three decimal places, we get c 5831 3 In this case, Q = ( 5,4,0), so we can say that xq = 5, yq = 4, and zq = 0 When we plug these values into the distancefromtheorigin formula, we get c = (xq2 + yq2 + zq2)1/2 = [( 5)2 + 42 + 02]1/2 = (25 + 16 + 0)1/2 = 411/2 A calculator approximates this irrational number to c 6403 4 This distance can be read straightaway from the graph if we use the z axis as a measuring stick If we want to go through the mathematics, we have R = (0,0,6), so we can assign xr = 0, yr = 0, and zr = 6 The distance formula yields c = (xr2 + yr2 + zr2)1/2 = (02 + 02 + 62)1/2 = 361/2 = 6 This value is exact 5 Line segment L connects points Q and R, where Q = (xq,yq,zq) = ( 5,4,0) and R = (xr, yr, zr) = (0,0,6) Plugging the coordinates into the formula for the distance d between two points in Cartesian threespace, we get d = [(xr xq)2 + ( yr yq)2 + (zr zq)2]1/2 = {[0 ( 5)]2 + (0 4)2 + (6 0)2}1/2 = [52 + ( 4)2 + 62]1/2 = (25 + 16 + 36)1/2 = 771/2 When we use a calculator to round this irrational number off to three decimal places, we get d 8775 6 Line segment M connects points P and R, where P = (xp,yp,zp) = (3, 3,4) 7
and R = (xr, yr, zr) = (0,0,6) Plugging the coordinates into the formula for the distance d between P and R gives us d = [(xr xp)2 + ( yr yp)2 + (zr zp)2]1/2 = {(0 3)2 + [0 ( 3)]2 + (6 4)2}1/2 = [( 3)2 + 32 + 22]1/2 = (9 + 9 + 4)1/2 = 221/2 A calculator rounds this value to three decimal places as d 4690 7 Line segment N connects points P and Q, where P = (xp,yp,zp) = (3, 3,4) and Q = (xq,yq,zq) = ( 5,4,0) The distance d between these points is d = [(xq xp)2 + ( yq yp)2 + (zq zp)2]1/2 = {( 5 3)2 + [4 ( 3)]2 + (0 4)2}1/2 = [( 8)2 + 72 + ( 4)2]1/2 = (64 + 49 + 16)1/2 = 1291/2 A calculator rounds this to three decimal places as d 11358 8 We want to find the midpoint of the line segment L connecting the points Q = (xq,yq,zq) = ( 5,4,0) and R = (xr, yr, zr) = (0,0,6) Let s call the midpoint A (for average ) in this situation, because we re already using M as the name of a line segment The midpoint formula tells us that the coordinates of A are (xa,ya,za) = [(xq + xr)/2,( yq + yr)/2,(zq + zr)/2] = {( 5 + 0)/2,(4 + 0)/2,(0 + 6)/2} = ( 5/2,4/2,6/2) = ( 5/2,2,3) 504 WorkedOut Solutions to Exercises: 19 9 We want to find the midpoint of the line segment M connecting the points P = (xp,yp,zp) = (3, 3,4) and R = (xr,yr,zr) = (0,0,6) If we again call the midpoint A, our formula tells us that the coordinates of A are (xa,ya,za) = [(xp + xr)/2,( yp + yr)/2,(zp + zr)/2] = [(3 + 0)/2,( 3 + 0)/2,(4 + 6)/2} = (3/2, 3/2,10/2) = (3/2, 3/2,5) 10 We want to identify the midpoint of the line segment N connecting the points P = (xp,yp,zp) = (3, 3,4) and Q = (xq,yq,zq) = ( 5,4,0) Let s call the midpoint A once more Plugging the values into the formula, we obtain the coordinates (xa,ya,za) = [(xp + xq)/2,( yp + yq)/2,(zp + zq)/2] = {[(3 + ( 5)]/2,( 3 + 4)/2,(4 + 0)/2} = ( 2/2,1/2,4/2) = ( 1,1/2,2)

