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EEL 3105 practice exam Solution_Corrected2

# EEL 3105 practice exam Solution_Corrected2 - EEL3105 1 x[2...

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EEL 3105 Solution Practice Problem Set 1. Consider the 6 dimensional vectors [ 2 1 3 1 2 ] [ 4 2 2 1 6] x a y b   (i) For this part, suppose a=2 and b=4. Calculate the scalar product of x and y. 1. 1 2. 2 3. 3 4. 4 5. 5 . 6 x y x y x y x y x y x y (ii) Suppose a=4. For what value of b will the scalar product be zero? . 2( ) 4 6 2 2 4( 6) 0 5 x y b b     (iii) Suppose the scalar product of x and y is 10. What can you say about values of a and b? . 2( ) 4 6 2 2 ( 6) 10 2 6 4 3 2 x y b a b a b a       Thus, a and b are any real numbers satisfying the equation b+3a=2. Clearly, there are infinitely many such choices. They lie on the straight line given by b+3a=2. (iv) Now suppose the Euclidean norm of x is 5. Find value(s) of a and b. 2 2 2 2 2 2 1 2 3 4 5 6 x x x x x x x 2 19 25 a 6 2 3 6 a b   2. Consider the vectors 2 1 3 2 3 1 2 1 x y   (i) Find the angle between x and y. First, note that x.y = 3, | | 18,| | 15 x y .

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