math 152 assig 1 - , 1) and b = (1 , 2 ,-3) in R 3 (the set...

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Math 152, Spring 2011 Assignment #1 Notes: Each question is worth 5 marks. Due in class: Monday, January 10 for MWF sections; Tuesday, January 11 for TTh sections. Solutions will be posted Tuesday, January 11 in the afternoon. No late assignments will be accepted. 1. Sketch axes x 1 - x 2 . Add the vectors (1,3) and (-3,-1) to your sketch. Draw these vectors with base point at the origin. Now add the vector (-3,-1) to your sketch, starting at the base point (1,3). That is, draw the vector with components 3 to the left and 1 down starting at (1,3). Note: your sketch should show graphically that (1,3)+(-3,-1)=(-2,2). 2. Consider the vectors a = (5 , 2
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Unformatted text preview: , 1) and b = (1 , 2 ,-3) in R 3 (the set of vectors with 3 components). Compute the following: (a) a + b (b) 2 a (c) a-b (d) a b (e) k b k 3. Describe and sketch the following set of points { s a : s [0 , 1] } where a is a non-zero vector in R 2 . That is, the set of scalar multiples of a where the scalar is between 0 and 1 inclusive. 4. Let a = (2 , 2 , 1) and b = (1 , 1 ,-2). Compute the following: (a) The angle between a and b . (b) proj a b (the projection of b in the direction of a ). 5. Determine the values of c 1 and c 2 such that the vector [ c 1 1 c 2 ] is a scalar multiple of [1 -2 2]....
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This note was uploaded on 03/30/2011 for the course MATH 152 taught by Professor Caddmen during the Spring '08 term at The University of British Columbia.

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