Plane and solid analytic geometry; an elementary textbook . eswith the axes, and the conditions for parallelism are 01 =o2, Pi = p2, and 71 = Y2. [11] PROBLEMS 1. Show that the three lines whose direction cosines are 12-3-4. 4 12 3 . orirl 3 -4 1 2T5> T^> T3 J T¥> T3> T3 J djllu T3J T3> T3 are mutually perpendicular. 2. Show that (3, 30°, 60°, 90°), and (5, 30°, 90°, 60°) arepossible polar coordinates of two points, and find the angle theysubtend at the origin. 3. Show that the conditions for parallelism are consistentwith [9] when 0 = 0°. 4. Find the rectangular coordinates of
Plane and solid analytic geometry; an elementary textbook . eswith the axes, and the conditions for parallelism are 01 =o2, Pi = p2, and 71 = Y2. [11] PROBLEMS 1. Show that the three lines whose direction cosines are 12-3-4. 4 12 3 . orirl 3 -4 1 2T5> T^> T3 J T¥> T3> T3 J djllu T3J T3> T3 are mutually perpendicular. 2. Show that (3, 30°, 60°, 90°), and (5, 30°, 90°, 60°) arepossible polar coordinates of two points, and find the angle theysubtend at the origin. 3. Show that the conditions for parallelism are consistentwith [9] when 0 = 0°. 4. Find the rectangular coordinates of the points inproblem 2. 5. Find the polar coordinates of the point (3, — 6, 2).. 6. Find the angle subtended at the point (1, 2, 3) by thepoints (2, 3, 4) and (5, 4, 3). 218 ANALYTIC GEOMETRY OF SPACE [Ch. I, § 10 9. Transformation of coordinates. Parallel axes. — Ifthe new axes are parallel to the old, and the coordinates of the new origin, re-ferred to the old axes, are(#0, y0, 20), the equationsof transformation areeasily seen (see Fig. 8). x to be ac = x0 + ocf V = 2/o + V, [12] Z = Z0 + Z . 10. Transformation of coordinates from one set of rec-tangular axes to another which has the same origin. — Let(«ii fiv Yj), («2, £2, 72), and («3, /33, y3) be the directionangles of OX\ OY\ andOZ with respect to theoriginal axes. The coor-dinates (#, y, 2) of anypoint P are the projec-tions of OP on OX, OF,and OZ. But the brokenline made up of x\ y!, andz extends from 0 to P,and will therefore havethe same projections on Ythe axes as OP. Hence(by Art. 5)
Size: 1726px × 1448px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookpublishernewyorkcscribnerss
