This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 < ∞ ....
View
Full
Document
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
 JEFFMORGAN

Click to edit the document details