Question

The angle between the planes $2x-3y-6z=5$ and $6x+2y-9z=4$ is

• A. ${\cos }^{-1}\left(\frac{30}{77}\right)$
• B. ${\cos }^{-1}\left(\frac{40}{77}\right)$
• C. ${\cos }^{-1}\left(\frac{50}{77}\right)$
• D. ${\cos }^{-1}\left(\frac{60}{77}\right)$

Answer 1

The correct option is D ${\cos }^{-1}\left(\frac{60}{77}\right)$

$P_1:2x-3y-6z=5P_2:6x+2y-9z=4$

Angle between plane is angle between normals.

$\therefore \cos \theta =\frac{2\times 6+(-3)\times 2+(-6)(-9)}{\sqrt{2^2+3^2+6^2}\sqrt{6^2+2^2+9^2}}=\frac{60}{77}$
$\theta ={\cos }^{-1}\left(\frac{60}{77}\right)$