Let L_1 and L_2 be two lines passing through the points P (b-c, c-a, a-b) and Q (1/l, 1/m, 1/n) respectively, where 1/l, 1/m and 1/n are the a^th,…

Let $\displaystyle \mathrm{L}_1$ and $\displaystyle \mathrm{L}_2$ be two lines passing through the points $\displaystyle \mathrm{P}(b-c, c-a, a-b)$ and $\displaystyle \mathrm{Q}$ $\displaystyle \left(\frac{1}{l}, \frac{1}{m}, \frac{1}{n}\right)$ respectively, where $\displaystyle \frac{1}{l}, \frac{1}{m}$ and $\displaystyle \frac{1}{n}$ are the $\displaystyle a^{\text {th }}, b^{\text {th }}$ and $\displaystyle c^{\text {th }}$ terms of an Arithmetic Progression. If $\displaystyle \mathrm{L}_1$ and $\displaystyle \mathrm{L}_2$ intersect at the origin, then an angle between them is