By J. P. Harnad, S. Shnider

ISBN-10: 3540100105

ISBN-13: 9783540100102

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Extra info for Geometrical and Topological Methods in Gauge Theories

Sample text

The 6. 4) pass (x^, y^) lies and (7, - 3) is divided Find the equation of the line joining line joining the points (6, 2) in the ratio of 2 to 5. the point (0, — 5) (—5, to the point of division. The coordinates of the vertices of a triangle are {2, 1), and (-4, - 1). Find the equation of the medians, and show that the coordinates of the point of intersection of 7. (3, - 2), any two medians satisfy the equation of the third, and that the three medians therefore meet in a point. What 8. are the equations of the diagonals of the rectangle whose vertices are (0, 0), (a, 0), (0, h), and (a, h) ?

Which are five ANALYTIC GEOMETRY 24 A 4. tlie [Ch. Ill, § 16 point moves so as to be always five times as far from I" axis as from the Find x)oint (5, 0). equation of tlie its locus. A 5. point moves so that the distances from the points Find the equation of 40. A 6. equation of A 7. A 8. (0, 0) sum (5, of the squares of its — 5) is always equal to its locus. point moves so as to be always three times as far from the point two axes and — (1, 2) as from the point (—3, sum point moves so that the is 4).

22 be given, — a point on ^' the line and the direction of the line, obtain its equation {x^, as ' follows: Let — we can y^ be the given point, and Fig. 29. let the direction of the line be determined by the angle 7 which it makes with 38 ANALYTIC GEOMETRY [Cn. IV, § 27 the positive direction of the ^-axis measured in the positive direction of rotation. KP In the triangle ifPjP, . ^„ „ Ch. IV, THE STRAIGHT LINE § 28] Oblique 28. — In coordinates. and [8] we have made use A rectangular. 89 deriving equations [7] of the fact that the axes are separate demonstration is therefore necessary in oblique coordinates.

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