Dot Product of Equilateral Triangle

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SUMMARY

The discussion focuses on calculating the dot product of two unit vectors, u and w, in an equilateral triangle configuration. The conclusion is that the dot product u dot w equals -1/2, derived from the cosine of the angle between the vectors, which is 120 degrees. Since u and w are unit vectors, their magnitudes are 1, simplifying the dot product calculation to the cosine of the angle directly. This confirms that the dot product of unit vectors can be expressed as the cosine of the angle between them.

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  • Knowledge of trigonometric functions, specifically cosine
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Homework Statement



In an equilateral triangle with sides u, v, w, where they are all unit vectors, find u dot w.

Homework Equations



u dot w = |u||w|cosθ

The Attempt at a Solution



The answer is ##\frac {-1} {2} ##

cos(120) = -1/2

Elsewhere, I read the statement that since these are already unit vectors then the dot products are simply the angles between them. What does this mean? Does something cancel out the |u||w| in the denominator? Or do |u||w| function to make the dot in terms of unit vectors so they would both be 1 in this case?

Nevermind, got it.
 
Last edited:
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mill said:
Elsewhere, I read the statement that since these are already unit vectors then the dot products are simply the angles between them.

...the dot products are the cosine of the angle between them.
 

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