Question

The angle between two plane is 3x+2y-z=7 and x-4y+2z=0 is

Answer 1

Answer:  114°

Step-by-step explanation:

$\overrightarrow{u}=\bigg\\\\\overrightarrow{v}=\bigg\\\\\\u\cdot v=3(1)+2(-4)+\ -1(2)\quad =-7\\\\|u|=\sqrt{3^2+2^2+(-1)^2}\quad =\sqrt{14}\\\\|v|=\sqrt{1^2+(-4)^2+2^2}\quad =\sqrt{21}\\\\\\\cos\theta=\dfrac{u\cdot v}{|u|\ |v|}\\\\\\\cos\theta=\dfrac{-7}{\sqrt{14}\cdot \sqrt{21}}\\\\\\\cos\theta=\dfrac{-1}{\sqrt6}\\\\\\\large\boxed{\theta=114^o}$