Class 12

Math

3D Geometry

Three Dimensional Geometry

Find a unit vector normal to the plane $x−2y+2z=6$.

Given equation in vector form is $r⋅(i^−2j^ +2k^)=6$

Here, $∣i^−2j^ +2k^∣=1_{2}+(−2)_{2}+2_{2} =9 =3$

$r⋅(31 i^−32 j^ +32 k^)=36 =2$

Required unit vector $=(31 i^−32 j^ +32 k^)$ which is normal to the given plane.