1.

The value of the determinant `|k a k^2+a^2 1k b k^2+b^2 1k c k^2+c^2 1|`is`k(a+b)(b+c)(c+a)``k a b c(a^2+b^(f2)+c^2)``k(a-b)(b-c)(c-a)``k(a+b-c)(b+c-a)(c+a-b)`A. `k(a+b)(b+c)(c+a)`B. `k abc (a^(2)+b^(2)+c^(2))`C. `k(a-b)(b-c)(c-a)`D. `k(a+b-c)(b+c-a)(c+a-b)`

Answer» Correct Answer - C
we have
`|{:(ka,,k^(2)+a^(2),,1),(kb,,k^(2)+b^(2),,1),(kc,,k^(2)+c^(2),,1):}|=|{:(ka,,k^(2),,1),(kb,,k^(2),,1),(kc,,k^(2),,1):}|+|{:(ka,,a^(2),,1),(kb,,b^(2),,1),(kc,,c^(2),,1):}|`
`=0+k |{:(a,,a^(2),,1),(b,,b^(2),,1),(c,,c^(2),,1):}|`
`=k(a-b) (b-c) (c-a)`


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