exam1111

# exam1111 - u = √ 3 i j and v =-√ 3 i j Find the angle...

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Name: Section: TA: Time: Math 10C. Midterm Exam 1 April 23, 2003 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (4 points) Find an equation for the sphere that passes through the point (3 , 9 , 9) and has center (2 , 5 , 1). # Score 1 2 3 4 Σ

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2. (a) (2 points) Let a = h 4 , - 1 i , b = h 1 2 , 2 i . Compute a · b , | a | , and | b | . (b) (1 point) Let
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Unformatted text preview: u = √ 3 i + j and v =-√ 3 i + j . Find the angle between u and v . (c) (1 point) Find a unit vector perpendicular to i-j + k . 3. (4 points) Find the vector equation for the line passing through the point (-1 , 2 , 2) and parallel to the line h x, y, z i = h , 1 , 1 i + t h 2 ,-3 , 3 i . 4. (4 points) Find an equation for the plane through the point (2 , 3 ,-5) and perpendicular to the vector h-3 , 4 , 1 i ....
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exam1111 - u = √ 3 i j and v =-√ 3 i j Find the angle...

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