2433midtermreview - Math 2433 Online Midterm Review Problem...

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Math 2433 Online Midterm Review Problem 1. (a) Given the points A (1 , - 2 , 1) ,B (3 , 2 , 2) ,C ( - 2 , 1 , - 5) ( i ) Prove that A,B and C are the vertices of a right triangle. ( ii ) Determine the length of the hypotenuse of the triangle. ( iii ) Find an equation for the sphere that has the hypotenuse for its diameter. ( iv ) Find an equation for the plane that contains A, B, and C . (b) Given the vectors a = 2 i - k , b = 2 i + 3 j - k , c = - i + 3 j - 2 k ( i ) Calculate: 3(2 a - b + c ) ( ii ) Find: proj b c ( iii ) Determine a unit vector in the direction of b × a . ( iv ) Determine the volume of the parallelepiped that has a , b , and c as sides. Problem 2. Given the plane P : 3 x - y + 4 z = 3, the line L : x - 1 - 2 = y + 4 2 = z + 3 2 , and the point A ( - 3 , 0 , 5): (a) Determine whether P and L are parallel. (b) Determine whether A lies on L . If is does not, find the distance from A to L . (c) Determine the parametric equations for the line M that passes through A and is perpendicular to P . (d) Find the point of intersection of
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2433midtermreview - Math 2433 Online Midterm Review Problem...

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