Vector dot product help.

  • Thread starter RadiationX
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  • #1
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i have three vectors: a=4,b=3,c=5 that form a right triangle.
vector a is in the positive x direction, vector b is in the positive y direction starting at the tip of a. vector c is the hypotenuse of the triangle with tip at the origin. (see attaced picture .doc file)


the questions are: what is a dot b, a dot c, and b dot c.


i have the solutions in my manual but i dont understand them.


the manual says that from the figure it is clear that a + b + c = 0, where a is perpindicular to b:


a dot b = 0, since the angle between them is 90 degrees:


a dot c = a dot (-a-b)=-|a|^2=-16

and similarly b dot c = -9

i have no idea whay this is true. any help would be appreciated especially a general explanition of what the dot product is
 
Last edited:

Answers and Replies

  • #2
dextercioby
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Is that a joke...?You posted only 2... :tongue2:

Daniel.
 
  • #3
cronxeh
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A dot product between vector a and vector b is this:

a dot b = |a|*|b|*cos(theta)
a dot b = (AxBx)i + (AyBy)j + (AzBz)k

Those are two definitions and they are equal. In your case, you are given the lenght of vectors (a=4,b=3,c=5). This is the called the magnitude of a vector. the |a| = 4, |b| = 3, |c| = 5. How would you find the angle theta between the two vectors?

There are two laws you can use. Law of sines and law of cosines. Or a pythogoras' theorem if the vectors form a right angle. In your case the triangle is right, because 4^2 + 3^2 = 5^2. So you can use a good old SOH CAH TOA rule (Sin = Opposite/Hypothenus, Cos = Adjacent/Hypothenus, Tan = Opposite/Adjecent).

Try to visualize the triangle first. Obviously c is a hypothenus with lenght 5.

This is given: |a| = 4, |b| = 3, |c| = 5
And you want to find:
1] a dot b = |a|*|b|*cos(theta)= 4*3*cos(90) = 0
2] a dot c = |a|*|c|*cos(theta) = 4*5*4/5 = 16
3] b dot c = |b|*|c|*cos(theta) = 3*5*3/5 = 9
 
Last edited:
  • #4
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ok i made my mistake with soh cah toa , but the last two answers are -16 and -9. why the negative sign? thx
 
  • #5
Doc Al
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RadiationX said:
why the negative sign?
Because the angle between the vectors ([itex]\theta[/itex]) is 90 < [itex]\theta[/itex] < 180 degrees, a region in which [itex]cos \theta[/itex] is negative.
 
  • #6
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dot product

Doc Al said:
Because the angle between the vectors ([itex]\theta[/itex]) is 90 < [itex]\theta[/itex] < 180 degrees, a region in which [itex]cos \theta[/itex] is negative.

i'm not saying that your're wrong but how do you know that cos is in the second quad? from the picture this is not obvious.
 
  • #7
Doc Al
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To find the angle between two vectors, redraw them so that their tails start at the same point. Direction matters!
 
  • #8
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that's it!!! thank you Doc AI
 

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