Question

The smaller angle (in degrees) between the planes x + y + z = 1, and 2x -y + 2z = 0 is_______

• A. 54.73

Answer 1

The correct option is A 54.73
x + y + z = 1
and 2x - y + 2z = 0

cos $\theta$ = $\frac{A.B}{\left|A\right|\left|B\right|}$
cos $\theta$ = $\frac{2-1+2}{\sqrt{3}.\sqrt{9}}$
cos $\theta$ = $\frac{3}{3\times \sqrt{3}}$

$\theta$ = $co{s}^{-1}\left(\frac{1}{\sqrt{3}}\right)$
$\theta$ = ${54.73}^{\circ }$