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The Vector Unit Test (not the unit vector test) Fall 2012 MI-4 Name: ________________________ You may use your TI-89 calculator, but you must show all set-up for credit. 1) (2 pts. each) True or false (no work necessary): _____ A plane is traveling at 475 miles per hour in the direction N35W. The velocity vector of the plane is given by 475 cos(125), 475 sin(125). _____ If |v| = |w| and v̂ = ŵ then v = w. a _____ |v| = vv. _____ In the diagram at right, a + b = c. b c 2) Given vectors x a,2 and y 2a 1, 5 . a) (3 pts.) Find all values of a that make these vectors perpendicular to each other. b) (3 pts.) Find all values of a that make these vectors parallel to each other. MI4 Vector Exam 1 Fall 2012 3) Consider the vectors p = 1, 4 and q = –2, 2. a) (2 pts.) Draw and label p and q. b) (1 pt.) Compute pq. c) (2 pts.) Compute projpq. d) (1 pt.) Compute p̂ . e) (2 pts.) Compute |2p – 3q| f) (1 pt.) Find a vector of length 8 with the same direction as p. MI4 Vector Exam 2 Fall 2012 4) (5 pts.) A pilot desires to fly in the direction S55E at a speed of 450 knots. There is a wind blowing at 30 knots in direction N20E. At what speed and directionshould the pilot fly to compensate for the wind? 5) (5 pts.) Two wires hold up a prop in a movie set, as shown at right. The angles that the wires make with the ceiling are 35 and 60, and the tension in the wire with the 60 angle is |T2| = 400N. What is the tension |T1| in the other wire? And what is the mass of the prop? Reminder: the magnitude of g is 9.8 m/s2. 35 T1 60 T2 prop –mgj jj MI4 Vector Exam 3 Fall 2012 6)a) (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) a) (2 pts.) Givenr the two vectors a and b below, sketch a b . b) (2 pts.) Given ther two vectors a and b below, sketch projar b a a b 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 2012