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Mathematical Investigations IV 2013 Vector Unit Test Name:_____________________ Mods __________ You may use a calculator on this exam, but must show all set-up. I should be able to recreate your answer from your work. 1) If v 2,6 and w 3,5 . Find: a) Find v̂ , the unit vector in the direction of v . b) Find the measure of the angle between v and w c) Find projv w . 2) For what values of a will the angle formed by 3,5 and a,6 be obtuse? 3) For what values of a will the vectors 2a, a 4 and 1,a be orthogonal? Mathematical Investigations IV 2013 Vector Unit Test Name:_____________________ Mods __________ 3) Given a 3, 4, 2 and b 2,5,0 , a) Sketch a . z y b) Find 2a 3b x 4) Let v and w be as drawn. Sketch the following vectors, clearly labeling your work. a) v 2w w v b) proj v w w v Mathematical Investigations IV 2013 Vector Unit Test Name:_____________________ Mods __________ 5) The object shown in the figure is hanging in equilibrium, with |T1| = 20 Newtons and |T2| = 25 Newtons. We know T1 T2 0, mg 0,0 . 20cos(30 ) 25cos( ) 0 Hence, 20sin(30 ) 25sin( ) 9.8m |T1| = 20 N 30 |T2| = 25 N -mgj (g = 9.8 m/s2) Determine the measure of angle and the mass, m, of the object. Round your answers to the nearest tenth. Using the trusty TI 89 to solve gives 46.2 and m 2.9 kg 4 pts 6) Find the scalars (a, b) such that w au bv if w 15,32 , u 2, 1 , and v 3,5 . w au bv 15,32 a 2, 1 b 3,5 2a 3b 15 a 5b 32 a 3 and b 7 Mathematical Investigations IV 2013 Vector Unit Test Name:_____________________ Mods __________ 7) Given a regular hexagon ABCDEF with center O, u AG 1 AF and v AB (see figure 2 below), find each of the vectors in terms of u and v . 2 pts a. CD 2u 2 pts 2 pts b. AO v 2u 2 pts c. AE v 4u d. E CA CO OA v AO v v 2u 2v 2u D O F C G u v B A