Find the dot product of the vectors and using the equation

Please show complete working out of how to do the above. Any attempt to do so will be appreciated.

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- September 5th 2009, 08:52 PMMr Rayonmultiplying two vectors - the dot product
Find the dot product of the vectors and using the equation

Please show complete working out of how to do the above. Any attempt to do so will be appreciated. - September 5th 2009, 09:16 PMJML
To do this question in the specified way you need to find the lengths of both vectors and then the angle between the vectors. If then the same method is used for the length of v.

If the question did not specify the method you had to use for the dot product it would likely be easier to calculate the dot product as follows:

say we have

then:

- September 5th 2009, 09:40 PMMr Rayon
- September 5th 2009, 09:47 PMmr fantastic
- September 5th 2009, 09:55 PMJML
You can find the angle by noting the coordinates that the vector would end at if it started at the origin.

so let's say and . So for**a**we get the point A =(3,3) and for**b**we get the point B=(6,2) . First we find the angle between the line x=0 (the**i**direction) and the line that passes through the origin and A, this angle = . You can do something similar for the other vector. You can then find the angle between the vectors by subtracting the angle to B from the angle to A. - September 5th 2009, 10:15 PMMr Rayon
and

Okay, I've drawn a diagram...and then I find the difference between the angles:

,

,

I am lost from here, and is the above right? Can somebody provide complete working out?

EDIT: I don't know what I'm doing here. - September 5th 2009, 10:37 PMmr fantastic
- September 5th 2009, 10:41 PMJML
,

so

so

- September 6th 2009, 03:55 AMHallsofIvy