Midterm_and_Solutions

# Midterm_and_Solutions - MIDTERM EXAM ON CALCULUS III...

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MIDTERM EXAM ON CALCULUS III 6:15pm–7:50pm, July 22, 2010 Your Name : Note that no book, lecture notes or calculators are allowed during the midterm and we denote a vector by a letter in boldface, such as a , b , v , i , j , k . There are totally 4 questions valued 60 points and a bonus question valued 5 points. 0

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MIDTERM EXAM ON CALCULUS III 1 Question 1. Given three points A,B,C R 3 . A = (1 , 0 , 0) , B = (0 , 2 , 0) and C = (0 , 0 , 3) . (15 points) (1) Find the vector a going from A to B and the vector b going from A to C . (2) Find a × b and ﬁnd cos BAC . (3) Find the area of the triangle 4 ABC . Solution: (1)(4 points) a = (0 - 1 , 2 - 0 , 0 - 0) = ( - 1 , 2 , 0); b = (0 - 1 , 0 - 0 , 3 - 0) = ( - 1 , 0 , 3). (2) (6 points) a × b = ± ± ± ± ± ± ± i j k - 1 2 0 - 1 0 3 ± ± ± ± ± ± ± = 6 i + 3 j + 2 k ; cos BAC = a · b | a || b | = 1 50 or 1 5 2 ; (3)(5 points) S 4 ABC = 1 2 | a × b | = 7 2 . ±
2 MIDTERM EXAM ON CALCULUS III Question 2. Given three points A,B,C R 3 . A = (1 , 0 , 0) , B = (0 , 2 , 0) and C = (0

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## This note was uploaded on 02/27/2011 for the course MATH 101 taught by Professor Y during the Spring '11 term at Columbia College.

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Midterm_and_Solutions - MIDTERM EXAM ON CALCULUS III...

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