anonymous
  • anonymous
Find the area of the parallelogram with the defining vectors i) a=( 4,-5) and b= (7,2) ii) a= (4,-5,3) and b= (7,2,-4)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
subtract one vector from the other to get it to the origin; is my first thought
amistre64
  • amistre64
but my first thought aint always too good :)
amistre64
  • amistre64
|dw:1327355180731:dw|

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amistre64
  • amistre64
maybe better idea. magnitude of b * height; where height is the "a"sin(a)
amistre64
  • amistre64
the determinate of the vector matrix of the first one would be good, but not work out to well for the second
amistre64
  • amistre64
i can recall the dot product stuff for cos(t) but never for sin(t) for some reason
anonymous
  • anonymous
Thank you!!
amistre64
  • amistre64
The cross product a × b is defined as a vector c that is perpendicular to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span. from the wiki i think
amistre64
  • amistre64
so |axb| seems to be the area of the parallelogram if im reading this right
amistre64
  • amistre64
now i gotta recall how to cross a 2component vector
amistre64
  • amistre64
3 components i can do :)
amistre64
  • amistre64
ii) a= (4 -5 3) and b= (7 2 -4) --------------- x = 20-6 = 14 y=-(-16-21) = 37 z = 8+35 = 43 sqre them add them and sqrt them for magnitude; might wanna use a calcultor :)
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=sqrt%2814%5E2%2B37%5E2%2B43%5E2%29 58.5 thereabouts?
amistre64
  • amistre64
cross was good; i can wolf the other one for simplicities sake too
amistre64
  • amistre64
determinant of the vector matrix on 1 is 43, with any luck i recalled that stuff right
anonymous
  • anonymous
woowww thank you soo soo much!! :)
amistre64
  • amistre64
do we know if i was right? lol

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