quiz2_sols_1 - (P2): 2x + y -2z = 5 intersect. It is given...

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QUIZ 2 Name: REMEMBER!! Show details of your work and use correct notation. 1. (6 points) Let u =< 4, -3,1 > and v = 2i + 4j + 4k. Find: a)The dot product of u and v. "'.v~ cg-l-'\. .t"Lt=o .... - b)The cross product ?f u a. .nd v. f 1. J U. \( \1- .... ,..- "'" ')C .......... I Li -3 , ; -f~~ - \4 j t~l,~ "" ,.., 2 .., "1 c)What is the angle between u and v 2. (8 points) Find the equation of the plane through the points A(I, -2,3), B( -2,1,2) and C(-4,-1,2). A~ :: - ~ ~ + ~ 1 - ~ ,A t z: - S" ~ -to L- !i 4~ ~ A<- ~ l-~ l ~ 1 ~ -1.~ ... 1 i t \t.~ 3 -s , -( 1" 'v- , t-"\ L r, }~) -1. (}C-I) t 2.(--:>-+1) t ,t(=l. -'S) = D ",( 3. (6 points) Find parametric equations for the line in which the planes (PI) : 3x- 6y - 2z = 15 and
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Unformatted text preview: (P2): 2x + y -2z = 5 intersect. It is given that nl x n2 =< 14,2,15 > where 'n} and 'n2 arc the normal vectors to the planes (PI) and (P2) respectively. ~I 1-~'\,. :;: t : "", ,1., \5", '1) ---V ~C+".r .J:~""' t.R.J( -t~ "-~ p t..-ne.l ') t;~ e, ~ {. ;'1 teA'S e. (.1"." 1 . l ° ~ i, l __ ~+-.0 Y\ .,. . ~ .t'11., ~L c.~~ + .... II~ "'j rOll\-COW"tr"v'l ~ .}-\. .L.-+1fJ'-' ~~~) " -\$ 'ot t 1l{. . ~~ ~ ~ 0 t ~ {?> )' -'j: ~ 1..)' 1" J -...vL r e. ~ )(;;' 3) '1 :::.-, s, tvi'\~ f~r r--\. '3>, -\ )~) .Q. ..i-t. .l 0, +l. ..-\t-V\ t L } ~ poi . ., .t--\~ l,. ... tA"IL i , ~ "'L--.. .c i "t-c. 'l!~~4-14 ) 'j-:-lf2-t-, l. .=-\{ ..t...
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This note was uploaded on 02/25/2010 for the course MATH 201 taught by Professor Kim during the Spring '07 term at SIU Carbondale.

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