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Unformatted text preview: Math 20C Practice Midterm 1 Lin Place all books and papers under your desk. You may have a 3 × 5” card of handwritten notes. On the cover of your blue book write your name, student ID number, section time, and color of your exam. In a column number one to five. Show all your work and give reasons for your answers. Box your answers. 1. (a) 5 pts. Find the area of the parallelogram PQRS with P = (0 , 1 , 2), Q = (4 , 1 , 1) ,R = (1 ,- 1 , 3). Also find the coordinates of the point S of the parallelogram. (b) 7 pts. The figure below illustrates two tugboats pulling a barge. If tugboat A exerts a force of 5000 pounds, what force must tugboat B exert if the barge is to move along the straight line l ? (c) 5 pts. Find the equation of the plane containing the points P (1 , 2 ,- 1) , Q (3 , 4 , 2) , R (- 1 , , 4). (d) 5 pts. Suppose vectora is perpendicular to vector b = < 1 , 2 , 3 > and vector c = <- 1 , , 2 > . What is vectora · (2 vector b + 3 vector c )?...
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- Fall '10
- pts, Euclidean geometry