Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the angle between the planes $r⋅(3i^−4j^ +5k^)=0$ and $r⋅(2i^−j^ −2k^)=7$.

The given planes are $3x−4y+5z=0$ and $2x−y−2z=7$.

Let $θ$ be the angle between the planes.

The direction ratios of normals to these planes are $3,−4,5$ and $2,−1,−2$

$∴cosθ={3_{2}+(−4)_{2}+5_{2} }{2_{2}+(−1)_{2}+(−2)_{2} }∣(3×2)+(−4)×(−1)+5×(−2)∣ =0$

$⇒θ=2π $.