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the area of the triangle whose vertices ...

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

Text Solution

Verified by Experts

The correct Answer is:
`sqrt13`
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`
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