anonymous
  • anonymous
vectors
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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ganeshie8
  • ganeshie8
use dot product and find any two angles of the triangle
ganeshie8
  • ganeshie8
|dw:1378466435271:dw|
anonymous
  • anonymous
i know dot product but which vertices do i need to multiply

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ganeshie8
  • ganeshie8
|dw:1378466476558:dw|
ganeshie8
  • ganeshie8
call the given points A, B C
ganeshie8
  • ganeshie8
join A, B, C to form a triangle
ganeshie8
  • ganeshie8
|dw:1378466562043:dw|
ganeshie8
  • ganeshie8
your task is to find wat type of triangle it is
anonymous
  • anonymous
ya so now do i need to find vector AB
ganeshie8
  • ganeshie8
start by finding angle A
ganeshie8
  • ganeshie8
exactly, observe that angle A is the angle between vectors AB and AC
ganeshie8
  • ganeshie8
so you just need to take dot product between vectors AB and AC to find angle A
anonymous
  • anonymous
ohk so wait a sec i am going to find ab ac ca cb bc and ba for all of them
ganeshie8
  • ganeshie8
hmm, finding two angles is enough.. third angle is implicit by triangle sum property
ganeshie8
  • ganeshie8
find ab ac ca cb to find angles A and C
anonymous
  • anonymous
alright ab and ac are -3 -3 5 and 2 13 -4 ba and bc are 3 -12 and -5 and 5 1 -9
anonymous
  • anonymous
what next
ganeshie8
  • ganeshie8
careful, check ab again
ganeshie8
  • ganeshie8
AB = (-1, 5, 8) - (2, -7, 3) = (-3, 12, 5)
ganeshie8
  • ganeshie8
others look correct
anonymous
  • anonymous
thx dudee....frikin algebra
ganeshie8
  • ganeshie8
:) next, to find angle A , take dot product of ab and ac
ganeshie8
  • ganeshie8
AB . AC = ||AB|| ||AB|| cos A
ganeshie8
  • ganeshie8
<-3, 12, 5> . <2, 13, -4> = ||<-3, 12, 5>|| ||<2, 13, -4>|| cos A
ganeshie8
  • ganeshie8
you can solve angle A
anonymous
  • anonymous
-6+156-20 = 13.342*13.748 cos a arc cos (135/( 13.342*13.748)) = 42.609
ganeshie8
  • ganeshie8
good :) find angle B also
anonymous
  • anonymous
hey whats that cos ormula for that
anonymous
  • anonymous
i mean for b as you gave me for a
ganeshie8
  • ganeshie8
|dw:1378467515650:dw|
ganeshie8
  • ganeshie8
angle B is between BA and BC, BA . BC = ||BA|| ||BC|| cos B
ganeshie8
  • ganeshie8
you have solved before, ba and bc are 3 -12 and -5 and 5 1 -9
ganeshie8
  • ganeshie8
plugin..
anonymous
  • anonymous
15-12+45 = 62.249*10.344 cos b theta = 85.725
anonymous
  • anonymous
so they are all acute
ganeshie8
  • ganeshie8
yes ! good work !! there is a simpler way of figuring this out... without having to work all this long...
anonymous
  • anonymous
ya man thx...this will help in exam
ganeshie8
  • ganeshie8
but save it for some other day... :) np you're wlcme :)
ganeshie8
  • ganeshie8
that simpler way is to decide the type of triangle based on performing oly the dot product. u can pursue this later..

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