This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Physics (PHZ) 3113 Florida Atlantic University Mathematical Physics Fall, 2009 Review Problems III Recommended Reading: Chow, pp. 1–13; Boas, Sections 3.4–3.5. 1. (Chow 1.2) Show that there is a unique plane in threedimensional 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 threedimensional vectors. a. Show that the three vectors are coplanar 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....
View
Full
Document
This note was uploaded on 10/21/2011 for the course PHZ 3113 taught by Professor Staff during the Fall '10 term at FAU.
 Fall '10
 STAFF

Click to edit the document details