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Using the property of determinants,show ...

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

Text Solution

Verified by Experts

`|[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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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
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  8. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  9. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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  10. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| On taking 2 ...

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  11. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| Evaluate De...

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  12. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  13. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  14. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 OperatingC1...

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  15. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 Solve the ...

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  16. Without expanding the determinant prove the following. |[x,a,x+a],[y...

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  20. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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  21. By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],...

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