the area of the triangle whose vertices are A ( 1,-1,2) , B ( 1,2, -1) ,C ( 3, -1, 2) is ________.

Answer

`sqrt13`

Explanation

Aera of `triangleABC = 1/2 |vec(BA)xxvec(BC)|`
`vec(BA)= -hati-2hatj + 3hatk`
`vec(BC)=hati-2hatj +3hatk`
`Area=1/3|{:(hati,hatj,hatk),(-1,-2,3),(1,-2,3):}|=1/2|6hatj+4hatk|`
`|3hatj +2hatk|`
`sqrt(9+4) = sqrt13`