HW#3 - MA 116 Calculus II HW 3 (Solutions) Due: March 4,...

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Unformatted text preview: MA 116 Calculus II HW 3 (Solutions) Due: March 4, 2011 1. Find the following by directly applying the definition of cross product, i.e., right-hand rule: a) i j k = d) k j i = b) j k i = e) ( ) j j i = c) ( ) i j j i = f) ( ) j j k = 2. Let , v x y = and cos sin , sin cos v x y x y = + + . Show the angle between v and v is . Using the definition of dot product we have cos v v v v = ( ) ( ) ( ) 2 2 2 2 (1) , cos sin , sin cos cos sin sin cos cos v v x y x y x y x xy xy y x y = + + = + + + = + 2 2 (2) v x y = + ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 (3) cos sin cos sin cos sin cos sin v x y x y x y x y = + + + = + + + = Putting (1), (2), and (3) into our definition of dot product we get cos cos . Since the dot product is only defined for 0 , cos is a one to one function for this given domain. Hence, = . = 3. Show that if u and v are any vectors, then the vectors v u u v + and v u u v are orthogonal....
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This note was uploaded on 10/09/2011 for the course MATHEMATIC MA116 taught by Professor Duboski during the Fall '11 term at Stevens.

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HW#3 - MA 116 Calculus II HW 3 (Solutions) Due: March 4,...

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