Answer:
Area \[=\frac{1}{2}|({{b}^{2}}-{{c}^{2}})+b({{c}^{2}}-{{a}^{2}})+c({{a}^{2}}-{{b}^{2}})|\] \[=\frac{1}{2}|a(b-c)(b+c)-{{a}^{2}}(b-c)-bc(b-c)|\] \[=\frac{1}{2}|(b-c)(a(b+c)-{{a}^{2}}-bc|\] \[=\frac{1}{2}|(b-c)(ab+ac-{{a}^{2}}-bc)|\] \[=\frac{1}{2}|(b-c)(a-b)(c-a)|\] this can never be zero as \[a\ne b\ne c\] Hence these point can never be collinear. Hence Proved.
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