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Unformatted text preview: MAT-NYC LAB #1 Vectors - Norm and dot product 1. Given ~u and ~v (see sketch), draw each of the following vectors on separate sketches using geometric constructions only. a) ~u + ~v b) ~u- ~v c) 2 ~u + ~v d)- ~u + 2 ~v e) the vector ~w such that 2 ~u + 3 ~v- ~w = ~ f) the vector ~w such that ~u + ~v + ~w = ~ 2. Let ~u = [1 ,- 2 , 3]. Sketch two geometric representatives of ~u , indicating clearly initial and final points. 3. a) Let P (- 1 , 2 , 2) and ~v = [1 , 2 ,- 1]. Find the point Q such that the vector- PQ has the direction opposite to ~v and the same length. b) Let P 1 (2 , 1 ,- 2) and P 2 (1 ,- 2 , 0). Find the coordinates of the point P which is one quarter of the way from P 2 to P 1 . 4. a) Let A , B and C denote the three vertices of a triangle. Let D be the midpoint of the segment BC . Show that- AD = 1 2 (- AB +- AC ). b) Use vectors to show that the median to the base of an isosceles triangle is also a height....
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This note was uploaded on 09/26/2011 for the course BIO 293 taught by Professor John during the Spring '11 term at Harvard.
- Spring '11