153-t4sol - Math 153 - Spring 2010 NAME Signature Test 4 19...

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Math 153 - Spring 2010 NAME Signature Test 4 19 May 2010 Answer the following questions. The answers must be clear, intelligible, and you must show your work. Provide explanation for all your steps. Your grade will be determined by adherence to these criteria. Use of books, notes and calculators is strictly forbidden. The point value of each problem is given in the left hand margin. (6 pts.) 1. Find the values of x such that the vectors h 3 ; 2 ;x i and h 2 x; 4 ;x i are orthogonal. Two orthogonal vectors have zero dot product, thus h 3 ; 2 ;x i ± h 2 x; 4 ;x i = 0 6 x + 8 + x 2 = 0 ( x + 2)( x + 4) = 0 Answer: x = ² 2 and x = ² 4. 1
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2. You are given two polar curves r = 2 + cos 2 ± and r = 2 + sin ± . a).(5 pts.) Prove that the intersection points of these curves have coordinates (5 = 2 ; 5 ²= 6) ; (5 = 2 ; ²= 6) ; (1 ; ± ²= 2) : Hint: the trigonometric formulas you need are provided on the last page. The intersection points can be found by solving for ± in the following equation: 2 + cos 2 ± = 2 + sin ± which can be rewritten as: 1 ± 2 sin 2 ± = sin ± and also as: 2 sin 2 ± + sin
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153-t4sol - Math 153 - Spring 2010 NAME Signature Test 4 19...

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