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# The angle between the planes $3x+4y+5z=3$ and $4x-3y+5z=2$ is ?

$\begin{array}{1 1} \frac{\pi}{2} \\ \frac{\pi}{3} \\ \frac{\pi}{4} \\ \frac{\pi}{6} \end{array}$

Toolbox:
• Angle between the two planes is $cos\theta=\large\frac{\overrightarrow n_1.\overrightarrow n_2}{|\overrightarrow n_1|\:|\overrightarrow n_2|}$
From the equations of the given two planes , $\overrightarrow n_1=(3,4,5)\:and\:\overrightarrow n_2=(4,-3,5)$
$\therefore\:$ Angle between them is given by $cos\theta=\large\frac{(3,4,5).(4,-3,5)}{\sqrt {50}.\sqrt {50}}$
$\Rightarrow\:cos\theta=\large\frac{25}{50}=\frac{1}{2}\:\:\therefore\:\theta=\large\frac{\pi}{3}$