An elementary treatise on coordinate geometry of three dimensions (1912)
Bell, Robert J. T. (Robert John Tainsh), 1877-1963 · London : Macmillan and co., limited · leaf 81
given lines is at right anglesto both, and it is therefore eqnal to the projection of AA ona line at right angles to both of the given lines. 58 COORDINATE GEOMETEY [CH. III. Suppose that A, /m, v are the direction-cosines of such aline, then l\-\-m/ui + nv = 0 and lX + m/a.-\-n,v = 0;X H mn — mn… … Fig. 24. Equation (7), §48, may now be interpreted as the con-dition that the shortest distance between the two givenlines should vanish. Again, if PP is the shortest distance,the equations to the planes APP, APP are ■13, Z-y n 0, x — a., y — 6, z — yV, m, n X, fj., 0, x — a., y-l, m, X, p., v and…
Geometry, Analytic
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