10c_04f_1be

# 10c_04f_1be - (a) a + ( b · c ) (b) a × b (c) u × v (d)...

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Math 10C First Midterm 40 points Oct. 18, 2004 PRINT NAME Write version on your blue book and VERSION B 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 2-sided page of notes. NO CALCULATORS are allowed. You may leave square roots in your answers, but NO trig functions. You must show your work to receive credit. 1. (12 points) In this problem, a , b and c are vectors in R 2 (the plane), u , v and w are vectors in R 3 (space) and s is a scalar. For each of the following, decide if it makes sense and: if it makes sense, describe the answer, for example, “a vector in R 3 ;” if it does not make sense, explain why, for example, “cannot cross product a vector and a scalar.”
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Unformatted text preview: (a) a + ( b · c ) (b) a × b (c) u × v (d) a · ( v × w ) 2. (12 points) Let a = 2 i + j be a vector in R 2 . (a) Find a vector in R 2 the same direction as a that has length 3. (b) Find a nonzero vector in R 2 that is perpendicular to a . 3. (6 points) A triangle has vertices A (1 , , − 1), B (0 , 3 , − 1) and C (3 , , 0). Find its area. 4. (5 points) Find an equation for the plane through the point (2 , − 1 , 1) and is perpen-dicular to the vector a 1 , 1 , 2 A . Do NOT leave vectors in your answer. 5. (5 points) Find the distance from the point (1 , 2 , 3) to the plane whose equation is (2 i − 3 j + k ) · r = 3. (As usual r = a x,y,z A = x i + y j + z k .) END OF EXAM...
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## This note was uploaded on 06/17/2009 for the course MATH 3412341 taught by Professor Staff during the Fall '06 term at UCSD.

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