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Practice_Problem_Exam 1

# Practice_Problem_Exam 1 - EEL 3105 Practice Problem Set 1 1...

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EEL 3105 Practice Problem Set 1 1. Consider the 6 dimensional vectors [ 2 1 3 1 2 ] [ 4 2 2 1 6] xa yb   (i) For this part, suppose a=2 and b=4. Calculate the scalar product of x and y. (ii) Suppose a=4. For what value of b will the scalar product be zero? (iii) Suppose the scalar product of x and y is 10. What can you say about values of a and b? (iv) Now suppose the Euclidean norm of x is 5. Find value(s) of a and b. 2. Consider the vectors     2 1 3 2 3 1 2 1 x y  (i) Find the angle between x and y. (ii) Define a new vector [1 1 1 1] w y a  . For what value of a will the scalar product of x and w be zero? (iii) Now suppose we change x and y to new vectors p and q such that their magnitude remains the same, i.e., ||x||=||p|| and ||y||=||q|| but the angle between p and q is twice the angle between x and y. Find the scalar product of p and q. 3. Let p, q, r be three dimensional vectors. Suppose the vector product of p and q is r, i. e.

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Practice_Problem_Exam 1 - EEL 3105 Practice Problem Set 1 1...

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