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Unformatted text preview: Physics (PHZ) 3113 Florida Atlantic University Mathematical Physics Fall, 2009 Review Problems III Recommended Reading: Chow, pp. 113; Boas, Sections 3.43.5. 1. (Chow 1.2) Show that there is a unique plane in three-dimensional space containing the vectors A := (2 ,- 6 ,- 3) and B := (4 , 3 ,- 1), and find a unit vector normal to it. 2. (Chow 1.7) Let A , B and C be three-dimensional vectors. a. Show that the three vectors are co-planar if and only if A ( B C ) = 0 . b. Find a necessary and sufficient condition for an arbitrary vector x to lie in the plane containing the points at the tips of A , B and C . 3. (Boas 3.4.4, 6 and 28) Prove the following theorems of plane geometry using vector algebra. a. The line segment joining the midpoints of two sides of any triangle is parallel to the third side and half its length. b. The lines joining the midpoints of opposite sides of a quadrilateral (any figure with four sides of arbitrary length with arbitrary angles between them) bisect each other.four sides of arbitrary length with arbitrary angles between them) bisect each other....
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