MAT267 – Test 1 – Fall2014 Math 267 – Test 1 Class Time:______________ Name: _________________________ Read all directions carefully! Be neat, and box all answers. Points will be deducted for not following directions, sloppiness or lack of relevant work shown. PLEASE NOTE: “Any student who accesses a phone or any internet-capable device during an exam for any reason automatically receives a score of zero on the exam. All such devices must be turned off and put away and made inaccessible during the exam.” Section I: Multiple Choice. Write your answers in the table provided. If you think the answer is “none of the above”, write in E. (6 pts each) (1) Which of the following are true: I. For any vectors u and v, ‖ ‖ ‖ ‖ ‖ ‖. II. For any vectors u and v , III. For any vectors u and v, . IV. For any vectors u and v, ( ) ( ) . A. I and II B. II and IV C. II, III, and IV D. They all are. E. None of these (2) Which of the following are true: I. In , if lines and are orthogonal to the same plane then they are parallel to each other. II. In , if lines and are parallel to a third line then they are parallel to each other. III. In , two lines either intersect or they are parallel IV. In , two planes either intersect or are parallel. A. I , II and IV. B. II and IV C. II, III, and IV D. They all are. E. None of these 3. Find the angle (in degrees) between the vectors and <2,-1,7>. (Round to two decimal places.) E. None of theseMAT267 – Test 1 – Fall2014 4. Find an equation of the plane through (2,1,3) that is parallel to the plane E. None of these 5. Which one of the following are parametric equations for the tangent line to the curve at the point ( )? A. B. C. D. E. None of these 6. Which vector is in the same direction as 〈 〉 and has length 6? 〈 〉 〈 〉 〈 〉 〈 〉 E. None of these 7. A force 〈 〉 moves an object from the point (0,1,2) to the point (3,6,1). Find the work (ignoring units). E. None of theseMAT267 – Test 1 – Fall2014 8. Which graph below corresponds to ? 9. Find the arc length of the curve: ( ) (√ ) where A. 6 B. √ C. 12 D. √ E. None of these 10. Which of the following points is closest to the yz-plane? A. ( ) B. ( ) C. ( ) D. ( ) Multiple Choice Table Question Answer 1 2 3 4 5 6 7 8 9 10MAT267 – Test 1 – Fall2014 Section II: Free Response. Show all work and be neat. (11) [10 pts] Determine whether the lines intersect , are skew, or are parallel. If they intersect determine the point of intersection; if not leave that part of the question blank. Circle One: Intersect or Skew or Parallel. Point of intersection: ___________________ (12) Decompose the vector 〈 〉 into two orthogonal vectors, one parallel to 〈 〉 and one orthogonal to . [10 pts] ___________________________ ___________________________MAT267 – Test 1 – Fall2014 (13) [10 pts] Find an equation of the plane through the points P(0,0,0), Q(0,1,0), R(1,2,3) Answer:_____________________________________ (14) [10 pts] Find the velocity and position vectors of a particle with acceleration ( ) and initial conditions ( ) and ( ) ( ) ___________________________ ( )