The acute angle between the planes P₁ and P₂, when P₁ and P₂ are the planes passing through the intersection of the planes 5x + 8y + 13z - 29 = 0 and 8x - 7y + z - 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

Equation of the plane passing through the line of intersection of  $5x+8y+13z-29=0\text{ and }8x-7y+z-20=0 \mathrm{is}$ $5x+8y+3z-29+\lambda (8x-7y+z-20)=0$ and if it  is passing through the point (2,1,3) then $\lambda =\frac{7}{2}$

$\begin{array}{l}5x+8y+3z-29+\frac{7}{2}(8x-7y+z-20)=0\\ \Rightarrow P_1=2x-y+z=6\end{array}$

Equation of the plane passing through the line of intersection of  $5x+8y+13z-29=0\text{ and }8x-7y+z-20=0$ and the point (0,1,2) is$x+y+2z=5$

$\text{ Angle between planes }=\theta ={\cos }^{-1}\left(\frac{3}{\sqrt{6}\sqrt{6}}\right)=\frac{\pi }{3}$