1. ## Geometric interpetation of the addition of two dot products???

Hi,

Let's assume that one needs to calculate the dot product between two 3 dimensional vectors (unit vectors) $\displaystyle u_1$ and $\displaystyle u_2$. This can otherwise be interpreted as finding the angle between them i.e. $\displaystyle \cos\psi_m$.

Further assume that another pair of 3 dimensional unit vectors exists $\displaystyle u_3$ and $\displaystyle u_2$. Note that one of the unit vectors is the same in both cases. The dot product between these two can also be expressed by the angle between them as $\displaystyle \cos\psi_n$.

What will be the result if I would like to add/substract these two angles $\displaystyle \cos\psi_m$ +- $\displaystyle \cos\psi_n$?

I would appreciate if someone could also explain me geometrically the implications of the addition/subtraction process. Is there any other way of expressing the result of the addition/substraction into a single term?

Thanks a lot

Regards

Alex

2. First, you need to be very sure that you understand that the dot product of two vectors is a number and not an angle. For unit vectors that number is the cosine of the angle between the vectors. If it is positive the angle is acute; if it is negative the angle is obtuse; if it is zero the angle is a right angle. As to you actual question, what does adding the cosines of any two angles with a common ray mean? Surely that are many different possible meanings.

3. Yeap I do know that the dot product between two vectors is a scalar. Lets say that the vectors are not orthogonal so that the cosine is not zero. So does the addition of $\displaystyle \cos\psi_n$with$\displaystyle \cos\psi_m$ have a geometrical meaning?
Can you please list some of those meanings?

Thanks again

Best Regards

4. Originally Posted by tecne
So does the addition of $\displaystyle \cos\psi_n$with$\displaystyle \cos\psi_m$ have a geometrical meaning?
I have idea.
What does 0.5 + 0.75 mean geometrically?
What does 0.25 - 0.5 mean geometrically?
What does cos(A)+cos(B) mean geometrically?