# HW 2 - Math E-21a Fall 2009 HW#2 problems Problems to turn...

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Math E-21a – Fall 2009 – HW #2 problems Problems to turn in on Thurs, Sept 17 : Basic Concept Problems : (a) Prove the Pythagorean Theorem . [ Hint : This can be done, for example, by considering the areas of plane figures like squares and triangles.] (b) Prove the Law of Cosines using only the Pythagorean Theorem and some algebra and trigonometry. You may find the diagram shown at the right useful. [Show that 2 2 2 C A B 2ABcos ] Section 9.3: 16. Find, correct to the nearest degree, the three angles of the triangle with the vertices D (0, 1, 1), E (–2, 4, 3), and F (1, 2,–1). 24. Find the scalar and vector projections of b onto a : 1,2 a , 4,1   b 25. Find the scalar and vector projections of b onto a : 3,6, 2 a , 1,2,3 b 37. Find the angle between the diagonal of a cube and one of its edges. 40. If c a b b a , where a , b , and c are all nonzero vectors, show that c bisects the angle between a and b . Section 9.4: 14. Find two unit vectors orthogonal to both i + j + k and 2 i + k .

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