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The Vector Unit Test (not the unit vector test) Fall 2015 MI-4 Name: ________________________ You may use your TI-89 calculator, but you must show all set-up for credit. 1. (3 pts) Dr. Torres is going to Springfield. He is travelling from IMSA at 63 mph in the direction S 23 W . Will he go through Bloomington given that the location of Bloomington (from IMSA) is given by the vector 50, 74 , where measurement are in miles? Explain clearly with a picture. 2. Given vectors x a, 2, a and y 2a, a 7, 6 . a) (3 pts.) Find all values of a that make these vectors orthogonal to each other. b) (3 pts.) Find all values of a that make these vectors parallel to each other. MI4 Vector Exam 1 Fall 2015 3. Consider the vectors p = 4,1 and q = 1,1 a) (2 pts) Draw and label p, q, and projqp b) (1 pt) Compute pq. c) (2 pts) Compute projqp. d) (1 pt) Compute p̂ . e) (2 pts.) Compute |2p – 3q| f) (1 pt) Find a vector of length 8 in the opposite direction of p. MI4 Vector Exam 2 Fall 2015 4. (8 pts) Given that BC is parallel to AD , 1 2 BC 2 AD w AB , u AD , and F is the 2 3 midpoint of BC , find each of the following vectors in terms of u and w . a. F B C w A D u BC b. AC c. FD d. CD 5. (5 pts) Two wires hold up the door to Dr. Condie’s office, as shown at right. The angles that the wires make with the ceiling are 30 and 55 , and the tension in the wire with the 55 angle is |T2| = 200N. Find the tension |T1| in the other wire and the mass of the door? Reminder: the magnitude of g is 9.8 m/s2. MI4 Vector Exam 3 T1 T2 door Fall 2015 6a) (2 pts.) In the shown grid at right. sketch v = 3, –2, 4. z b) (3 pts.) Find the angle between v = 3, –2, 4 and w = 0, 2, –3 to the nearest tenth of a degree. y x 7. (2 pts.) Given the two vectors a and b below, sketch a 2b . a b 8.(3 pts. ) If the vector v 3, 2 is rotated about the origin 50 in the clock-wise direction, find the resulting vector. MI4 Vector Exam 4 Fall 2015