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## Homework Statement

Three units vectors a, b, and c have property that the angle between any two is a fixed angle [tex]\theta[/tex]

(i) find in terms of [tex]\theta[/tex] the length of the vector v = a + b + c

(ii) find the largest possible value of [tex]\theta[/tex]

(iii) find the cosine of the angle [tex]\beta[/tex] between a and v

## Homework Equations

unit vector = vector with length 1unit

magnitude of vector = [tex]\sqrt{x^2+y^2+z^2}[/tex]

[tex]\cos \theta = \frac{r_1\cdot r_2}{|r_1||r_2|}[/tex]

## The Attempt at a Solution

(i) I think I get it right. The answer is [tex]\sqrt{3+6\cos \theta}[/tex]

(ii) I don't know how to do this. I think [tex]\theta < 90^o[/tex] , but I can't find the exact value

(iii)

[tex]\cos \beta = \frac{a\cdot v}{|a||v|}[/tex]

After some calculation,

[tex]\cos \beta = \frac{2+\cos \theta}{\sqrt{3+6\cos \theta}}[/tex]

Can it be simplified further?

Thanks a lot