math 101 assig1

math 101 assig1 - a = (1 , 2) and b = (1 ,-2) in R 2 (the...

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Math 152, Spring 2009 Assignment #1 Notes: Each question is worth 5 marks. Due in class: Monday, January 12 for MWF sections; Tuesday, January 13 for TTh sections. Solutions will be posted Tuesday, January 13 in the afternoon. No late assignments will be accepted. 1. Sketch axes x 1 - x 2 . Add the vectors (2,2) and (1,-1) to your sketch. Draw these vectors with base point at the origin. Now add the vector (1,-1) to your sketch, starting at the base point (2,2). That is, draw the vector with components 1 to the right and 1 down starting at (2,2). Note: your sketch should show graphically that (2,2)+(1,-1)=(3,1). 2. Consider the vectors
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Unformatted text preview: a = (1 , 2) and b = (1 ,-2) in R 2 (the set of vectors with 2 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 R } (that is, the set of all scalar multiples of a ) where a is a non-zero vector in R 2 . 4. Let a = (1 , 1 , 1) and b = (3 , 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 [2 -2 3]....
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