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Volume of tetrahedron formed by the planes `x+y=0, y+z=0, z+x=0,x+y+z-1=0` isA. `(1)/(6)`B. `(1)/(3)`C. `(2)/(3)`D. None of these |
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Answer» Correct Answer - C Solving the planes taking 3 at a time Vertices of tetrahedron are `O: (0,0,0), A: (1,1,-1),B:(1,-1,1),C:(-1,1,1)` `implies "Volume"=(1)/(3) xx("area of base")xx("height")` `=(1)/(3)xxsqrt(3)/(4)xx(2sqrt(2))^(2)xx(1)/sqrt(3)=(2)/(3)` Or Volume `=(1)/(6)[vec(a) vec(b) vec(c)]` `("where" vec(a)=vec(OA), vec(b)=vec(OB) and vec(c) = vec(OC))` |
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