21c_02f_1ae - 1 and C x 3 4 form the vertices of a right...

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Bender Math 21C First Midterm Oct. 21, 2002 PRINT NAME Write version on your blue book and VERSION A hand in this exam inside your blue book. Put your name, ID number, and section number (or time) on your blue book. You may have ONE PAGE of notes. NO CALCULATORS are allowed. You must show your work to receive credit. 1. (30 pts.) A curve is given parametrically by x =2 t 3 +3 t 2 - 1 and y = t 2 - 3 t + 2 for - 4 t 2 . (a) Write down an integral for the length of the curve. Do NOT evaluate the integral. (b) Find those points where the curve is VERTICAL ; that is, give their x and y coordinates. 2. (30 pts.) The three points A (2 , 1 , 0), B (1
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Unformatted text preview: , , 1) and C ( x, 3 , 4) form the vertices of a right triangle whose right angle is at A . (a) Find x . (b) Find the cosine of the angle whose vertex is C . 3. (40 pts.) Consider the two planes described as follows: First plane : It is perpendicular to the vector h 1 , 2 , i and contains the origin. Second plane : It contains the origin and the line given parametrically by h x, y, z i = t h 1 , 1 , i + h , 2 , i . (a) Write down equations for the two planes. (b) Write a parametric equation for line of intersection of the two planes. END OF EXAM...
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