
#1
Mar113, 05:42 PM

P: 61

I'm reading up on dot products and keep seeing two different examples.
One states that u[itex]\cdot[/itex]v = u[itex]_{i}[/itex][itex]\cdot[/itex]v[itex]_{i}[/itex] + u[itex]_{j}[/itex][itex]\cdot[/itex]v[itex]_{j}[/itex] Another: u[itex]\cdot[/itex]v = u[itex]\cdot[/itex]vcosθ I'm not understanding when to use the first or second method? 



#2
Mar113, 05:57 PM

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On the other hand, if you are given the lengths of the vectors and the angle between them, you can use the second equation to find the dot product. 



#3
Mar113, 05:59 PM

P: 61

Makes sense, I think the way the book I'm looking in words it was confusing me. Thanks




#4
Mar113, 07:47 PM

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Vector dot products
For example, if you are given that one vector is <1, 0, 0> and the other is <2, 2, 0> it is easy to calculate that the dot product is 1(2)+ 0(2)+ 0(0)= 2.
But if you are given that one angle has length 1, the other has length [itex]2\sqrt{2}[/itex], and the angle between them is [itex]\pi/4[/itex], it is easiest to calculate [itex](1)(2\sqrt{2})(cos(\pi'4)= 2[/itex]. By the way, in spaces of dimension higher than 3, we can use the "sum of products of corresponding components" to find the dot product between two vectors, then use [itex]uvcos(\theta)[/itex] to define the "angle between to vectors". 


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