|{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,...

`|{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,a+6):}|=0`

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Prove that the triangle formed by joining the points ( 2 , 3 , - 1) , ( 4 , 5 , 0) , ( 2 , 6 , 2) is and isosceles triangle .

The mean and S.D of 1, 2, 3, 4, 5, 6 is

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|{:(1,2,3),(4,5,6),(3,2,2):}|

|{:(2,3,4),(5,6,1),(3,2,3):}|

|{:(" "x+1," "-3," "4),(" "-5," "x+2," "2),(" "4," "1," "x-6):}|

|{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0
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|{:(a-b,1,a),(b-c,1,b),(c-a,1,c):}|=|{:(a,1,b),(b,1,c),(c,1,a):}|
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|{:(a+1,a+4,a+2),(a+2,a+5,a+4),(a+3,a+6,a+6):}|=0
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|{:(" "0," "a,b),(-a," "0,c),(-b,-c,0):}|
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|{:(9,9,12),(1,-3,-4),(1,9,12):}|=0
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|{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c...
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|{:(441,442,443),(445,446,447),(449,450,451):}|=0
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Prove |{:(cos(x-a),cos(x+a),cosx),(sin(x+a),sin(x-a),sinx),(cosa tan x...
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|{:(101,103,105),(104,105,106),(107,108,109):}|=0
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|{:(5^2,5^3,5^4),(5^3,5^4,5^5),(5^4,5^6,5^7):}|=0
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|{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)...
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|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)
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|{:(1,alpha,alpha^3),(1,beta,beta^3),(1,gamma,gamma^3):}|=(alpha-beta)...
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|{:(a+b+2c," "a," "b),(" "c,b+c+2a," "b),(" "c,...
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|{:(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=(b-c)(c-a)(a-b)(bc+ca+ab)
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|{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)
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|{:(a,b,c),(a^2,b^2,c^2),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)
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|{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xy+yz+zx+xyz
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|{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(x-4)^2
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|{:(1+a,1,1),(1,1+a,1),(1,1,1+a):}|=a^3+3a^2
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