The value of the subtle angle between the normal’s of the planes $2x - y + z = 6$ and $x + y + 2z = 7$ will be-

Explanation

$2x - y + z = 6$ here $a_1= 2, b_1 = -1, c_1 =1$ $x + y + 2z = 7$ here $a_2= 1, b_2 = 1, c_2 =2$ $Cos\theta = \frac{a_1a_2 + b_1b_2 + c_1c_2}{\sqrt{a_1^2 + b_1^2 + c_1^2}\sqrt{a_2^2 + b_2^2 + c_2^2}}$ $= \frac{2 - 1 + 2}{\sqrt{6}\sqrt{6}} = \frac{3}{6}$ $Cos\theta = \frac{1}{2} = Cos60^\circ = Cos \frac{\pi}{3}$ $\therefore \theta = \frac{\pi}{3}$