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Unformatted text preview: Name : PID : TA : Sec. No : Sec. Time : Math10C Midterm Exam October 29 2010 Turn off and put away your cell phone. No calculators or any other electronic devices are allowed during this exam. You may use one page of notes, but no books or other assistance during the exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write all your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # Points Score 1 6 2 6 3 6 4 6 5 6 30 Problem 1 (6 points): (a) Find the angle between the vectors ~a = 4 ~ i + ~ j and ~ b =- 2 ~ i + 8 ~ j . Are they parallel to each other, perpendicular to each other, or neither? Solution: The angle between the vectors is given by = cos- 1 ~a ~ b || ~a |||| ~ b || ! . Since ~a ~ b =- 8 + 8 = 0, then the vectors are perpendicular to each other, and the angle between them is 2 . (b) Find the equation of the sphere of radius 4 centered at the point (0 , 3 ,- 3) . Solution: The equation of the sphere is x 2 + ( y- 3) 2 + ( z + 3) 2 = 16 ....
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- Spring '07