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

Options

A. `sqrt(17)`
B. `13`
C. `sqrt(13)`
D. None of these

Answer

B

Explanation

Here `bar(OA)= hati-hatj+2hatkand bar(OB)= 2hati+hatj-hatk`
`and barc=3hati - hatj+2hatk`
`impliesbar(AB)=bar(OB)-bar(OA)=hati +2hatj- 3hatk and `
`bar(AC)=bar(OC)-bar(OA)=2hati`
Henve , the required area `=(1)/(2)|bar(AB)xxbar(AC)|`
`= bar(AB)xxbar(AC)=|{:(hati,hatj,hatk),(1,2,-3),(2,0,0):}|=-2(3hatj+2hatk)`
`implies` Area of triangle `=(1)/(2)xx2|3hatj+2hatk|=sqrt(13)`