# 09.07 - Hand out (and discuss) revised time-sheets (explain...

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Hand out (and discuss) revised time-sheets (explain A,B,C) Get contact info for new students Collect notes on 10.2 Section 10.1: Three-dimensional coordinate systems (concluded) Other examples to discuss: The set {( x , y , z ) | xyz = 0} is … ...?. . the three coordinate planes taken together. The set {( x , y , z ) | ( x –1) 2 +( y –2) 2 +( z –3) 2 = 0} is … ..?. . the “singleton” set consisting of the single point (1,2,3). The set {( x , y , z ) | ( x –1) 2 +( y –2) 2 +( z –3) 2 = –1} is … ..?. . the empty set (or null set) consisting of no points at all! The set {( x , y , z ) | ( x –1)/( x –1) = 1} is … ..?. . (remember, 0/0 is undefined!)

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..?. . the whole of space with the x =1 plane removed. Digression on set-notation: How can one write the set of numbers that are unequal to 1? { x R | x 1} { x : x 1} (– ,1) (1, ) R \ {1} (don’t worry about this one) Sometimes students write things like { x | x = R , x 1} or { x | R , x 1} or { x | (– ,1) (1, )} which aren’t “mathematically grammatical”. When you use the { x : …} or { x | …} notation, the “…” needs to be some property (or list of properties) of x , like x R or x 1, not a set like R or (– ,1) (1, ). Questions? Final challenge: What single equation corresponds to the
circle of radius 1 in the x , y plane, centered at (0,0,0)? Think about this for tomorrow. Section 10.2: Vectors Main ideas? ..?. . Definition of vectors Vector addition Scalar multiplication Parallel vectors Components of vectors Length of vectors Unit vectors Vectors are used for physical quantities that have magnitude and direction. Scalars are used for physical quantities that have magnitude but no direction.

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Which of the following are vector quantities, and which are scalar quantities? Speed
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## This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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09.07 - Hand out (and discuss) revised time-sheets (explain...

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