ubc math 200 midterm 1a 2011
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Math 200 sec. 103 (Bond) Exam1 (100 pts) Name: _
You have 50 minutes. Please show all work to get full credit.
1. (20 pts, 5 per part)u = <1 2 3> v = <-1 -1 5>'" , , .
a. Find lul and Ivl.
~j r'f~f£J.® J1~1f25 =\~8[iJrz~(+t-(L)H)+(jy» >-1-2-f15{3J ..c. Find the angle between u and v.
~~~~ I~llvl(oft
..0 20)-I U~v ...,1}J (oj li$f - -.I (0) IU~jd. Find uxv .
u-xV ::
...:;:. ~ ~
\ ) k.I 2 3-\ --~5
.; CQ)(S) -(3)(--1ilt - [(1)(')) -G)(-OJS
-t [ (I) (-1) - 0) HJ]f=- [lot- ~It - ['3-+31~T [-I+J-j
...> ->'.~ ~~'((V::: \) l -...,'6) +- ~
•••• ...;>
...• ~lA,'>I:V (1\ -Y,( I)
I
Math 200 sec. 103 (Bond) Exam} (100 pts) Name: _
2(25 pts): For this problem, A = (1,3,4) B = (3,3,1) C = (1,4,-3)
a) Find the area of the triangle whose corners are located at the pointsA, B, and C.
4~<2-0-3~!\ I / '/
,j(c =- <~JI/-t>
Aix~ c: (; J-f) =- 3~ +IY") +2~~ 0 I -+ ::: L;, I,2> ..
Find a non-zerolv) ogonal to the plane which contains
the three points A, B, and C.
\t) ftS.----
f;v
A rea -.:: , 1.-A ~Ij ABxjrc
~J~yJ~~ 5,1)
..::--l
,6ft),~ ~
r) =- AJ) x#:- =: 0,IQ/ :2>
c) Find an equation for the plane containing the three points A, B, andC.
-.:l ~11) 6 AP z: 0 I lAa--t- ~S)
< 3 I 1'1/1),,\>( -1!j -\ ? -4) -:::0---( 3(~-i) +h(~-3) ,})C2-t)~
~
. tr.
~::: (K;3?) '11\ -th flOYU-;
-----
Math 200 sec. 103 (Bond) Exam1 (100 pts) Name: _
® T'{jO ~ \ I'lh '. i.c:. (D -!:- () '\ f. 1 : v= ( -j 2X +') ~ --1=-1 ;i).---------- '>I SI ) . -
f - (J2- (I J) -- >( ~ j -+ 3 - J -~K~
I - SI 5; I;j :::.II <C
L II 9 - I \ x:--' I-: (t) ~ (1"~;)OPot tW,::: Q -t:) Z ~/-'>})) + t (ir3); . -5" - 5
.c----- ----
....-l ~
f\\~ ~l
2-3 -)--1
@( P~'~1-d-- \v~'t)d+~)
3. (25 pts) Consider two planes: Plane 1 has the equation2x + 3y -7z = 4, and Plane 2 has the equation x - y + 3z = 3.
a. (1Opts) Find the angle between the two planes.
if, = ()} I-f) (n, z: ,(\ -I) .)>-' ~ . il _ :=JEl~~
-;: ['1[\ InJ} (D.>G- 1 = ! ~ l·r--~ ~ ~ - Cd> (-22. , - V b)
- iLJ\T (G/8- - l~·b. (15pts) Find a para1netric equation tr the line where
Plane 1 intersects Plane 2.
I~h~::r"2-V;--
["'·ll ~~ ~ ~- \) -:: .. ~V :: Yll ~ ~ ~ - 1~--1 ~ II - \-3j --t; ~\ -- \ .5.--
f~L ~ lo:f) ~ ~ 2X-.¥3t(/'-{ 2(;jB)Hj 2 1{-
( x -'F-3~~. I <y +i o=-~~ \vI-r--3
x~J L~:= - 3,
A-~ f-~ ~ 135~ -S
f e::: (~-~ 0)/ $)
Of. - f ~~
< ~-=.l-0> + / 1 -) 3 - 5>-{:I >1 "I)
; --------~(-t)=-
Math 200 sec. 103 (Bond) Examl (100 pts) Name: _
4. (20pts) What is the shortest distance from the point (1,2,-3) tothe plane II whose equation is x - 3y + Z = 2? (0 tJ )
~ \:>0 ~ )?~~,le-s
p("O~~ (W)~
~ -0 \~~
r\\\ .
~jI)
p
-\0---~'~-I-I-~ 10---V1T
?(,)..~
fD P ~ <-0 2/ --S>~
//J -==- < 1)~3/1 )~ ~Rr f Y':: 1~-5
-=- - rD
/'
r; Math 200 sec. 103 (Bond) Examl (100 pts) Name: _
5. (1Opts) Consider the line A with the following parametricequations:
x = 2 -- 2t Y= 3 + 3t z = -5 -- tWhere does the line A intersect the plane 2x-y+z=4?
f\i'\~{ :
ll;-A) = 0~~t)1- (-S-t) ~i\ __~+ ~)- 3t -S ~ t- - ~
---Z~ - f c cr ,t- =-- -I
~
~~i ~:: V l =-~
f -= lLfIO / -~)
L _ .~
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