Engineering Calculus Notes 55

Engineering Calculus Notes 55 - bisect the three interior...

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1.3. LINES IN SPACE 43 and x = 3 t 1 y = t 2 z = t ; (b) x = t + 4 y = 4 t + 5 z = t 2 and x = 2 t + 3 y = t + 1 z = 2 t 3 . Theory problems: 7. Show that if −→ u and −→ v are both unit vectors, placed in standard position, then the line through the origin parallel to −→ u + −→ v bisects the angle between them. 8. The following is implicit in the proof of Book V, Proposition 4 of Euclid’s Elements [ 27 , pp. 85-88] . Here, we work through a proof using vectors; we work through the proof of the same fact following Euclid in Exercise 11 Theorem 1.3.3 (Angle Bisectors) . In any triangle, the lines which
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Unformatted text preview: bisect the three interior angles meet in a common point. Note that this is diferent from Theorem 1.3.2 in the text. Suppose the position vectors of the vertices A , B , and C are a , b and c respectively. (a) Show that the unit vectors pointing counterclockwise along the edges of the triangle (see Figure 1.24 ) are as follows: u = b a v = c b w = a c...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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