Question

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

Answer 1

Answer: 114°

Explanation:

`\overrightarrow{u}=\bigg<3, 2, -1\bigg>\\\\\overrightarrow{v}=\bigg<1,-4,2\bigg>\\\\\\u\cdot v=3(1)+2(-4)+\ -1(2)\quad =-7\\\\|u|=√(3^2+2^2+(-1)^2)\quad =√(14)\\\\|v|=√(1^2+(-4)^2+2^2)\quad =√(21)\\\\\\\cos\theta=(u\cdot v)/(|u|\ |v|)\\\\\\\cos\theta=(-7)/(√(14)\cdot √(21))\\\\\\\cos\theta=(-1)/(\sqrt6)\\\\\\\large\boxed{\theta=114^o}`