(Solved): Q2. A set of three mutually perpendicular axes in a body for which the product of inertia about the ...

Q2. A set of three mutually perpendicular axes in a body for which the product of inertia about these axes are zero are known as the principal axes of inertia of the body. They are given by the solution of the following determinantal equation: \[ \left|\begin{array}{ccc} I_{x x}-1 & I_{x y} & I_{x z} \\ I_{y x} & I_{y y}-1 & I_{y z} \\ I_{z x} & I_{z y} & I_{z z}-1 \end{array}\right|=0 \] Find the principals axes of moments of inertia of a body for which \( \mathrm{I}_{x x}=15, I_{y y}=25 \), \( I_{z z}=12, I_{x y}=I_{y x}=6, I_{x z}=I_{z x}=-8, I_{y z}=I_{z y}=4 \).