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assig1 - a =(3 2 and b =-1 2 in R 2(the set of vectors with...

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Math 152, Spring 2010 Assignment #1 Notes: Each question is worth 5 marks. Due in class: Monday, January 11 for MWF sections; Tuesday, January 12 for TTh sections. Solutions will be posted Tuesday, January 12 in the afternoon. No late assignments will be accepted. 1. Sketch axes x 1 - x 2 . Add the vectors (3,2) and (-2,1) to your sketch. Draw these vectors with base point at the origin. Now add the vector (-2,1) to your sketch, starting at the base point (3,2). That is, draw the vector with components 2 to the left and 1 up starting at (3,2). Note: your sketch should show graphically that (3,2)+(-2,1)=(1,3). 2. Consider the vectors
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Unformatted text preview: a = (3 , 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 , 4 , 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 [1 2 8]....
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