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# sn3_1 - Math 2433 Notes Week 3 Popper003 1 Find a set of...

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Math 2433 Notes – Week 3 Popper003 1. Find a set of scalar parametric equations for the line that passes through P (1, 3, -4) and is perpendicular to the xz -plane. a) b) c) d) e) f) None of the above. 2. Find an equation in x , y , z for the plane that passes through the given points. P (1, -1, 3), Q (2, -1, 2), R (2, 0, 3) a) b) c) d) e) f) None of the above. 13.1 Vector Functions Graphs: Vector functions in 3 R are in the form: 1 2 3 ( ) ( ) ( ) ( ) f i j k t f t f t f t = + + where f 1 , f 2 , and f 3 are the component functions. The scalar functions would take the form: 1 0 1 2 0 2 3 0 3 ( ) ( ) ( ) f t x d t f t y d t f t z d t = + = + = + The domain of a vector function is the set of all t ’s for which all the component functions are defined. It is the largest possible interval for which all three components are defined. Example: Find the domain of f ( t ) = cos t i + ln(4 – t ) j + 1 t +

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In order to sketch the graph of a vector function, it is easier to look at it in terms of the scalar vectors: 1 2 3 ( ) ( ) ) ) ( ) ( ) ( ) x t f t y t f t z t f t = = = Lets look at ( ) 2cos( ) 2sin( ) 3 r i j k t t t = + + Now let’s change that third component function to be 3 ( ) f t t =
(Winplot time!!)

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