Print your first and last name neatly in the box below and in the box at the bottom of every page. Name: Date: Please read the following directions carefully: • This exam contains 9 pages (including this cover page) and 12 questions. The point total is 80 points. Write your answers only in the space provided under each question, if at all possible. If you need more room, attach additional pages and clearly label the question you are answering/continuing. • After you complete the exam, you will create one pdf document containing all pages of your submission to upload to Canvas. Please make sure your pages are in order and combined into one pdf document. You may scan your work or use an iPad/tablet that will annotate this pdf, but it is your responsibility to make sure your work is clear and legible on the pdf you turn in. Illegible work/scans will not receive any credit. This is a closed-book, closed-note, individual exam, with the exception of one two-sided 3 × 5 inch index card. No other outside help is allowed (e.g. no book, no other notes, no internet, no discussing/communicating with others, except the instructor). Cell phones, laptops, and other technological devices are not allowed. Scientific calculators are allowed but not graphing calculators. • Answer all questions analytically with exact answers, unless the directions indicate otherwise. (Do not give rounded decimal approximations.) • Responses to short answer questions that do not include comprehensive work/justification will receive no credit. (Exceptions include questions that explicitly state that no work/justification is required.) Partial credit will be given on questions that require justification for any correct work that is presented. You must use correct mathematical notation that clearly communicates your logic and reasoning to receive credit. You MTH-2210-01 should also include appropriate units when applicable and clearly label any diagrams, charts, tables, or graphs that you provide in your answers. Illegible answers will not receive credit. Also, if you have extraneous scratch work in the designated answer space, make sure to mark out anything you don't want graded and clearly mark/indicate your final answer along with any required justification. On problems with multiple parts, clearly separate and label each part. • After you finish the exam, please sign and date the honor pledge below. Your exam cannot be graded if you do not sign below. Exam 1 - Page 2 of 9 Honor Pledge: I have read and understood these directions, and I certify that I have neither given nor received any unauthorized assistance nor used any unauthorized resources on this exam. Further, I pledge that my conduct on this exam is in full compliance with Belmont's Honor Code. Signature: Name: Date: MTH-2210-01 Exam 1 - Page 3 of 9 1. (5 points) Find the equation of the sphere that passes through the point (7, 2, −3) and has center (2,-1, 1). (Show any work below and then write your final answer in the box provided.) 2. Show whether each pair of vectors is orthogonal, parallel, or neither. If neither, find an exact expression for the angle between them. (You can leave the angle in the form arccos (...).) (Show your work below each part and then, in the box provided, write “orthogonal," "parallel," or the angle you calculated.) (a) (4 points) = (7,-5, 1), v= (6, 0, -1) u (b) (4 points) = (3,-1, 3), = (5, 9,-2) Name: MTH-2210-01 3. (5 points) Let ā = (–5, 12) and 6 = (4, 6). Find the vector projection of bonto a. (Show your work below and then write your final answer in the box provided.) proja (6) = 4. Let ƒ = i +33 + 4k and ĝ = 2ī + 73 − 5k. Find each expression. (Show your work below each part and then write your final answer in the box provided.) (a) (3 points) 3ƒ – 2g = (b) (3 points) fx g = Exam 1 - Page 4 of 9 (c) (2 points) gxf = Name: (You may use your answer from above instead of starting from scratch.) MTH-2210-01 Exam 1 - Page 5 of 9 5. (4 points) Find an equation for the plane that includes the point (9,-4,-5) and is parallel to the plane z = 2x - 3y. (Show your work below and then write your final answer in the box provided.) 6. (5 points) Find parametric equations for the tangent line to the space curve with the given equation at the specified point. (Show your work below and then write your final answer in the box provided.) r(t) = (t cos(t), t, tsin(t)); (-π, π, 0) Name: