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The area of the triangle whose vertices are `A(1,-1,2),B(2,1-1)C(3,-1,2)` is …….A. `sqrt(17)`B. `13`C. `sqrt(13)`D. None of these |
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Answer» Correct Answer - B 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)` |
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