This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 Excerpt: ... Cz + D = 0, finding the values of I, m, n, and p, and substituting in (4), we have as the magnitude of the required distance, being positive for all points on one side of the plane and negative for all points on the other side. If we choose, we may take the sign of the radical always positive, in which case we can ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 Excerpt: ... Cz + D = 0, finding the values of I, m, n, and p, and substituting in (4), we have as the magnitude of the required distance, being positive for all points on one side of the plane and negative for all points on the other side. If we choose, we may take the sign of the radical always positive, in which case we can determine for which side of the plane the above result is positive by testing for some one point, preferably the origin. Ex. 2. Find the distance of the point (1, 2, 1) from the plane 2x--3y + 6 z + 14 = 0. The required distance is Furthermore the point is on the same side of the plane as the origin, for if (0, 0,0) had been substituted, the result would have been 2, i.e. of same sign as 2. 3. Plane through a given line and subject to one other condition. Let the given line be J Multiplying the left-hand members of (1) and (2) by and k2 respectively, where and k2 are any two quantities independent of x, y, and z, and placing the sum of these products equal to zero, we have the equation Equation (3) is the equation of a plane, since it is a linear equation, and furthermore it passes through the given straight line, since the coordinates of every point of that line satisfy (3) by virtue of (1) and (2). Hence (3) is the required plane, and it may be made to satisfy another condition by determining the values of ftj and appropriately. Ex. 3. Find the equation of the plane determined by the point (0, 1, 0) and the line 4x + 3y + 2z-4 = 0, 2x-Uy-4z-12 = 0. The equation of the required plane may be written fci(4x + 3y+2z-4) + fc2(2x-lly-4z-12) = 0. (1) Since (0, 1, 0) is a point of this plane, its coordinates satisfy (1), and hence fci + 23fc2 = 0, or fci =-23fcjj. Substituting this value of fci in (1) and reducing, we have as the required equation Qx +...
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Add this copy of A Course in Mathematics, for Students of Engineering to cart. $24.35, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
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Add this copy of A Course in Mathematics, for Students of Engineering to cart. $37.96, new condition, Sold by Books2anywhere rated 5.0 out of 5 stars, ships from Fairford, GLOUCESTERSHIRE, UNITED KINGDOM, published 2022 by LEGARE STREET PR.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
Add this copy of A Course in Mathematics, for Students of Engineering to cart. $40.17, new condition, Sold by Paperbackshop International rated 2.0 out of 5 stars, ships from Fairford, GLOS, UNITED KINGDOM, published 2022 by LEGARE STREET PR.
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