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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:
`sqrt(13)` sq units
Area of `Delta ABC = (1)/(2) |vec(AB) xx vec(AC)|`
`vec(AB) = hat(i) + 2hat(j) - 3hat(k) " and " vec(AC) = 2hat(i) + 2hat(j) - 3hat(k)`
`:. , vec(AB) xx vec(AC) = |{:(hat(i),,hat(j),,hat(k)),(1,,2,,3),(2,,0,,0):}| = 2(-3hat(j) -2hat(k))`
`rArr` Area of triangle `=(1)/(2) | vec(AB) xx vec(AC)|`
`=(1)/(2) . 2 . sqrt(9+4)=sqrt(13)` sq units
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