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Unformatted text preview: MATH 2433 FINAL EXAM REVIEW QUESTIONS Problem 1. (a) The points (3 ,- 1 , 2) and (- 1 , 3 ,- 4) are the endpoints of a diameter of a sphere. ( i ) Determine the center and radius of the sphere. ( ii ) Find an equation for the sphere. (b) Given the vectors a = 2 i- j + 2 k , b = 3 i + 2 j- k , c = i + 2 k . ( i ) Calculate 2 a · ( b- 3 c ). ( ii ) Determine the vector projection of c onto b . ( iii ) Find the cosine of the angle between a and b . ( iv ) Find a unit vector that is perpendicular to the plane determined by a and c . Problem 2. Given the planes P 1 : 2( x- 1)- ( y + 1)- 2( z- 2) = 0 , P 2 : 4 x- 2 y + 5 z = 3, and the point Q : (- 2 , 7 , 4). (a) Determine whether P 1 and P 2 are parallel, coincident, perpendicular, or none of the preceding. (b) Find an equation for the plane through Q which is parallel to P 1 . (c) Determine scalar parametric equations for the line through Q which is parallel to the line of intersection of P 1 and P 2 . Problem 3. The position of an object at time t is given by: r ( t ) = e- t i + e t j- t √ 2 k , ≤ t < ∞ (a) Determine the velocity and the speed of the object at time t . (b) Determine the acceleration of the object at time t . (c) Find the distance that the object travels during the time interval o ≤ t < ∞ ....
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This note was uploaded on 07/20/2010 for the course MATH 11278 taught by Professor Jeffmorgan during the Fall '10 term at University of Houston.
- Fall '10