Exam 1 Spring 11

# Exam 1 Spring 11 - b onto a where a = h-2 3-6 i and b = h...

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MAC 2313-EXAM 1 NAME UF ID 1. Find the parametric equations of the line through (2 , 1 , 0) and perpendicular to both i + j and j + k . 2. Find the parametric equations for the line that goes through the points P ( - 2 , 4 , 0) and Q (6 , - 1 , 2). 3. The surface with equation - x 2 + 4 y 2 - z 2 = 4 is called a(n) . 4. Prove that ( a - b ) × ( a + b ) = 2( a × b ) 5. Find a vector valued function for the space curve given by the line segment from P (1 , 3 , 2) to Q ( - 4 , 3 , 0). 1

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6. Find a vector that has the same direction as h- 2 , 4 , 2 i but has length a > 0. 7. Find an equation of the sphere if one of it’s diameters has end points (2 , 1 , 4) and (4 , 3 , 10). 8. Prove that if r is a vector valued function such that r 00 exists, then d dt [ r ( t ) × r 0 ( t )] = r ( t ) × r 00 ( t ) 9. The work done by a force F along a displacement vector D is given by W = The torque that results from a force F acting on a rigid body at a given point with position vector r is given by τ = 10. Find the vector projection of

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Unformatted text preview: b onto a where a = h-2 , 3 ,-6 i and b = h 5 ,-1 , 4 i 2 MAC 2313 — EXAM 1 Free Response NAME SECTION UF ID YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE CREDIT!! 1. Find the equation of the plane that passes through the point (-1 , 2 , 1) and contains the line of intersection of the planes x + y + z = 2 and 2 x-y + 3 z = 1. 3 2. Given the vector valued function r ( t ) = ± t, cos 2 t, sin 2 t ² , we deﬁne the tangential and normal acceleration by the following a T ( t ) = r ( t ) · r 00 ( t ) | r ( t ) | = a N ( t ) = | r ( t ) × r 00 ( t ) | | r ( t ) | = ﬁnd the tangential and normal acceleration at the point (1 , , 1) (Hint: A trigono-metric identity along the way could save a lot of time) 4...
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## This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.

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Exam 1 Spring 11 - b onto a where a = h-2 3-6 i and b = h...

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