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quiz 1 answers - -3(15 points Let u =<-2,1,2> v = i 3j...

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QUIZ 1 Name: ~ (;-"/ REMEMBER!! Show deta.ils of your work and use correct notat.ion. 1. (10 points) Given u =< -l,3a,2 > and v =< 2,5,-4 >, determine all numbers a such that a)u and v are orthogonal. ~. V ~V -21"1'S~_~=O ;) "X ..... 0{ = 2/ 3 b)u and v are parallel. v- -'l~ - - 1.. <= -I ~ _1 2 "> -:") L2)),-Y,") - J 0\ I £2,5,-4)= L. 2. - 601 ~ - 't? '"'\r - 'V J -60( ~ ~ .=) - - - ~ 6 2. (5 points) Show that the equation x 2 + y2 + Z2 + 2x - 8y - Z + 16 = 0 represents a sphere, and find its center and radius. 1. 2- ()! ?- -r 2..,. tl} I ( j _ <:j?:{ r 16 ) + (~ - t -t ~ ) ;:: - 1 {, t' f ,e; t l y 'L 1.- ''L t~ tl) t () - 4) -f- C 2 - :t ) ~ 5/ 4 ( -) ) ~ It) : (.(2. vt t ~ 'Ii ..
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Unformatted text preview: --3. (15 points) Let u =< -2,1,2 >, v = i - 3j - k and let P(-1,4,2) be a point. Find: a)The dot product of u and v. _ 2 . \ 1" l (-» + 2. C.-I) -2- 3-2. -=--1-~ b)A vector of magnitude 5 poinLing in the direction of u . }i h> ~ ,. 5" ---~ .!::. -1 ~ oJ J + ~O __ ~ 3 __ ~ , ~\ c)A vector having magnitude three times thaL of u and pointing opposite u. -.3 l.( ""'" d)An equation of the plane through P and perpendicular to v , (;< t,) -~( j_ 4 -(1:-1) o y.. -~ j '1-::.--l S e)A vector w such that u+2w=3v 2w= 3 V -\A ,..", ..." ---'IV = ~ L 3 f -~ ) 1. ..... , ( 5 ~-I OJ -S" ~ ) w -"-'l-"--2...
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