Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Equation of OPQ is $\left|\begin{array}{lll}x& y& z\\ 1& 2& 1\\ 2& 1& 3\end{array}\right|=0$ $\Rightarrow 5x-y-3z=0$ equation of PQR is $\left|\begin{array}{ccc}x-1& y-2& z-1\\ 2-1& 1-2& 3-1\\ -1-1& 1-2& 2-1\end{array}\right|=0$ $\Rightarrow x-5y-3z+12=0$ Angle between the planes $\begin{array}{rl}& \theta ={\cos }^{-1}\left(\frac{5\times 1+(-1)\times (-5)+(-3)\times (-3)}{\sqrt{5^2+(-1{)}^2+(-3{)}^2}\cdot \sqrt{1^2+(-5{)}^2+(-3{)}^2}}\right)\\ & \Rightarrow \theta ={\cos }^{-1}\frac{19}{\sqrt{35}\cdot \sqrt{35}}={\cos }^{-1}\left(\frac{19}{35}\right)\end{array}$