The unit vector perendicular to the plane determined by P (1,-1,2) ,C(3,-1,2) is ________.

Answer

`(2hati+ hatj +hatk)/sqrt6`

Explanation

Required unit vector
`hata= (vec(PQ)xxvec(PR))/(|vec(PQ) xx vec(PR)|)`
`vec(PQ) = hati-hatj -3hatk, vec(PR)= -hati+3hatj-hatk`
`vec(PQ)xx vec(PR)=|{:(hati,hatj,hatk),(1,1,-3),(-1,3,-1):}|`
` 8hati + 4hatj + 4hatk`
`|vec(PQ) xx vec(PR)|=sqrt(64+16+16)=sqrt96 + 4sqrt6`
`hatn = (8hati+4hatj+4hatk)/(4sqrt6)=(2hati+hatj+hatk)/sqrt6`