Mathematics 1229A/B Midterm Oct,2007

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Use the following for questions 1,2 and 3. Let u = (2, 1, 4, 3) and v = (1, 1, 1, 0). Solution: the dot product of 2 vectors (in m-space for any m 2) is given by summing the products of corresponding components. D: 1 (2, 1, 4, 3) (1, 1, 1, 0) = (2)(1) + ( 1)( 1) + 4( 1) + 3(0) = 2 + 1 4 + 0 = 1. Solution: the di erence vector is simply the vector whose components are the di erences of corresponding components. Use the following for questions 4,5 and 6. Let v = (1, 1, 2) and w = (3, 1, 1). Solution: using the formula for (or any of the tricks for calculating) the cross product of two vectors in. 3 we get the vector (1, 1, 2) (3, 1, 1) = ((1)(1) (1)( 2), ( 2)(3) (1)(1), (1)(1) (3)(1))

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