ex1_fall11_2313

# ex1_fall11_2313 - Name MAC 2313 Exam 1 Version A SHOW ALL...

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Name: MAC 2313 Exam 1 Version A 09/02/2011 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [3]1. A vector has initial point P (2 , - 1 , 3) and terminal point Q (1 , 0 , - 4). Find its components and a unit vector with the same direction. [3] 2. The vector v lies on the xy - plane and makes an angle of π 4 with the positive x - axis, | v | = 5, ﬁnd v in component form. [3] 3. Find the equation of the sphere that has points ( - 2 , 5 , - 1) and (6 , 7 , - 3) as endpoints of a diameter.

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a) Two lines parallel to a third line are parallel. b) Given two lines they must either intersect or be parallel. c) Two lines perpendicular to a third line must be parallel. [4] 5. Consider the vectors v = 3 i - 7 j and w = - 2 i + c j , where c is some real number. a) Find a value of c such that v and w are orthogonal. b) Find a value of c such that v and w are parallel. [5] 6. Find the area of the triangle with formed by the vectors
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ex1_fall11_2313 - Name MAC 2313 Exam 1 Version A SHOW ALL...

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