1.

Using the property of determinants,show that the points A(a,b+c),B(b,c+a), C(c,a+b) are collinear.

Answer»

SOLUTION :`|[x_1, y_1,1],[x_2, y_2,1],[x_3, y_3,1]|=|[a, B+c,1],[b, c+a,1],[c, a+b,1]|`
`=|[a+b+c, b+c,1],[a+b+c, c+a,1],[a+b+c, a+b,1]|`
(by `C_1rarrC_1+C_2)`
`=(a+b+c)|[1, b+c,1],[1, c+a,1],[1, a+b,1]|=0`
`(because C_1=C_3)`
Thus, the given points are collinear.


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