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.

- anonymous

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- amistre64

I get it up to the point m(vector a) is m a scalar then?

- anonymous

yes

- amistre64

we can just say that Bv is <0,4> right? thats a vecotr of magnitude 4 :)

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## More answers

- amistre64

no we cant, we have to base it off of A... and 60 degree from it.... back to the draing pad :)

- amistre64

A<3,4> : ||A|| = 5

- anonymous

i found that (vector a) dot (vector b)= 10

- amistre64

by process of the math? or looking at the answers :)

- anonymous

process of math

- 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

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

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

vectors that are perpendicular have a dot product of zero.

- amistre64

[m<3,4> + b] * b = 0

- amistre64

do we know what the vector parts for b are? I was working on that :)

- anonymous

no we dont

- amistre64

we can figure it out :) do we need to?

- anonymous

yeah, i think so,

- amistre64

heres what I got from what we know.

##### 1 Attachment

- amistre64

b has 2 options up and to the left, or down and to the right.

- amistre64

the original angle of "a" is tan-1(4/3) = 53.1301

- amistre64

b has an angle of either -6.8699
or
b has an angle of 113.1301

- amistre64

4sin(t) will give us the y value and 4cos(t) will give us the x values right?

- anonymous

yeah

- 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

the other option for b is <3.97128, -.47846>

- amistre64

since we cant move a :) we need to work with these 2 possibilities and see what we get :)

- amistre64

Do you know if we should include the m in the vector like this?
+ < x , y > "b1"
------------

- anonymous

ok i think i can take it from here

- amistre64

itd a been nice if they had given us a pretty angle to work with off of "a" lol

- anonymous

yeah i know, vector is very difficult to deal with

- amistre64

if you got it from here....good luck :)

- amistre64

you can pick whichever vector for b gets you that 10 ;)

- anonymous

thank you very much for your help

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