A physical system has dynamical variables $X,Y,Z$ represented by the $2\times2$ Pauli matrices $\sigma_x,\sigma_y,\sigma_z$.
Compute the average value of $\ell X + m Y + n Z $ in any one state in which $a X + b Y + c Z $ has a definite value. Assume $\ell^2 + m^2 +n^2=1$ and $a^2 + b^2 + c^2=1$.
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4727:Diamond Point
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