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 Vector Dot Product problem
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dmmathwiz
Average Member

USA
7 Posts

Posted - 09/06/2007 :  21:37:59  Show Profile

....../\........(periods only used to keep spacing)
...../..\c......
...d/....\......
.../......\.....
../......./b....
./_______/......
.....a..........

is where vector 'a' and 'b' meet.
is where vector 'b' and 'c' meet.

Find an equation relating the lengths, d,a,b,c, and the angles , and for figure above.
Your expression should give d as a function of a, b, c, cos, cos, and cos(+).

HINT: use the vector dot product and vector sum relation.

I need help, i am assuming you set up an addition equation of the vectors to add up to d. Then i guess you need some how get it in the form of the stuff in the question.
THANKS
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dmmathwiz
Average Member

USA
7 Posts

Posted - 09/08/2007 :  14:26:01  Show Profile
I came up with

d * cos( + ) = a + bcos + ccos

any ideas?
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sahsjing
Advanced Member

USA
2399 Posts

Posted - 09/08/2007 :  19:06:39  Show Profile
quote:
Originally posted by dmmathwiz


....../\........(periods only used to keep spacing)
...../..\c......
...d/....\......
.../......\.....
../......./b....
./_______/......
.....a..........

is where vector 'a' and 'b' meet.
is where vector 'b' and 'c' meet.

Find an equation relating the lengths, d,a,b,c, and the angles , and for figure above.
Your expression should give d as a function of a, b, c, cos, cos, and cos(+).

HINT: use the vector dot product and vector sum relation.

I need help, i am assuming you set up an addition equation of the vectors to add up to d. Then i guess you need some how get it in the form of the stuff in the question.
THANKS



Hint:
Assume and are interior angles.
a, b, c, d are all vectors.
d = a + b + c
x direction:dx = a - bcos() - ccos(+-)
y direction:dy = bsin + csin(+-)
d = (dx + dy)

Edited by - sahsjing on 09/08/2007 20:28:44
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dmmathwiz
Average Member

USA
7 Posts

Posted - 09/10/2007 :  22:53:35  Show Profile
well thank you for all you help it was very helpful.

my teacher said to take the approach
d.d = (a+b+c) . (a+b+c)

all letters are vectors, all "."'s are dot product.

i ended up getting

d = a+b+c+2a.b+2a.c+2b.c

which i then substituted in the definition of dot products.
That is just the approach he wanted us to take, not sure how i would have come up with that, but i guess it works.
Thanks Again.
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