Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the angle between the planes $r⋅(i^+j^ )=1$ and $r⋅(i^+k^)=3$.

Given planes are $x+1=1$ and $x+z=3$

The direction ratio of normals to these planes are $1,1,0$ and $1,0,1$

$∴cosθ={1_{2}+1_{2}+0_{2} }{1_{2}+0_{2}+1_{2} }∣(1×1)+(1×0)+(0×1)∣ $

$=(2 ×2 )1 =21 $

The angle between the planes is

$⇒θ=3π $.