anonymous
  • anonymous
let a and b two vectors such that vector a = 3i + 4j, and the magnitude of vector b = 4, where the angle between the given vectors is 60*. If the vector (m(vector a)+vector b) is perpendicular to vector b, find the value of m.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
I get it up to the point m(vector a) is m a scalar then?
anonymous
  • anonymous
yes
amistre64
  • amistre64
we can just say that Bv is <0,4> right? thats a vecotr of magnitude 4 :)

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amistre64
  • amistre64
no we cant, we have to base it off of A... and 60 degree from it.... back to the draing pad :)
amistre64
  • amistre64
A<3,4> : ||A|| = 5
anonymous
  • anonymous
i found that (vector a) dot (vector b)= 10
amistre64
  • amistre64
by process of the math? or looking at the answers :)
anonymous
  • anonymous
process of math
amistre64
  • amistre64
can you type it out so I can see it :) that way I know what we both are looking at.... get me up to speed.
anonymous
  • anonymous
cos 60= 1/2 1/2= ((vector a) dot (vector b))/(magnitude of vector a * magnitude of vector b) 1/2= ((vector a) dot (vector b))/4*5 1/2= ((vector a) dot (vector b))/20 ((vector a) dot (vector b)) = 10
amistre64
  • amistre64
to keep things clean; we can use a to mean vector a and b likewise. magnitude is |a| works good. cos(60) = 1/2 1/2 = a*b / |a| |b| 1/2 = a*b / 4*5 1/2 = a*b /20 a*b = 10 ..good work :)
amistre64
  • amistre64
vectors that are perpendicular have a dot product of zero.
amistre64
  • amistre64
[m<3,4> + b] * b = 0
amistre64
  • amistre64
do we know what the vector parts for b are? I was working on that :)
anonymous
  • anonymous
no we dont
amistre64
  • amistre64
we can figure it out :) do we need to?
anonymous
  • anonymous
yeah, i think so,
amistre64
  • amistre64
heres what I got from what we know.
1 Attachment
amistre64
  • amistre64
b has 2 options up and to the left, or down and to the right.
amistre64
  • amistre64
the original angle of "a" is tan-1(4/3) = 53.1301
amistre64
  • amistre64
b has an angle of either -6.8699 or b has an angle of 113.1301
amistre64
  • amistre64
4sin(t) will give us the y value and 4cos(t) will give us the x values right?
anonymous
  • anonymous
yeah
amistre64
  • amistre64
the left vector option is <-1.57128, 3.67846> for "b" that gives us an angle betwwen them of 60 and a magnitude of 4
amistre64
  • amistre64
the other option for b is <3.97128, -.47846>
amistre64
  • amistre64
since we cant move a :) we need to work with these 2 possibilities and see what we get :)
amistre64
  • amistre64
Do you know if we should include the m in the vector like this? + < x , y > "b1" ------------
anonymous
  • anonymous
ok i think i can take it from here
amistre64
  • amistre64
itd a been nice if they had given us a pretty angle to work with off of "a" lol
anonymous
  • anonymous
yeah i know, vector is very difficult to deal with
amistre64
  • amistre64
if you got it from here....good luck :)
amistre64
  • amistre64
you can pick whichever vector for b gets you that 10 ;)
anonymous
  • anonymous
thank you very much for your help

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