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If p,q,r are not in G.P. and {:|(1,q/p...

If p,q,r are not in G.P. and
`{:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),(palpha+q,qalpha+r,0)|=0` then prove that `palpha^2+2qalpha+r=0`

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3.

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  2. Prove that : {:|(a^2a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b...

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  3. If p,q,r are not in G.P. and {:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),...

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  4. Using determinant , find the area of triangle with verticles (1,0) ,...

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  5. Using determinants find the area of triangle with vertices (1,-1), ...

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  6. Find the area of the triangle with vertices at the points given in eac...

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  7. Find area of the triangle with vertices at the point given in the fol...

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  8. Find area of the triangle with vertices at the point given in the fol...

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  9. Using determinants, show that the following points are collinear: (1...

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  10. Using determinants, show that the following points are collinear: (-...

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  11. If the point (3,-2),(x,2),(8,8) are collinear, find 'x' using determin...

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  12. if area of triangle is 35sq.unit with vertices (2,-6) (5,4) and (K,4) ...

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  13. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  14. Determine the value of 'x' for which the area of the triangle formed b...

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  15. Find equation of line joining (1, 2) and (3, 6) using determinants.

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  16. Find equation of line joining (3, 1) and (9, 3) using determinants.

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  17. Find the equation of the line joining A(1, 3) and B (0, 0) using deter...

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  18. Prove that area of the trianlge whose vertices are (at1^2,2at1) , (at2...

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  19. Prove that the (a, b+c), (b, c+a) and (c, a+b) are collinear.

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  20. If the oints (a1b1),(a2b2) and (a1-a2,b1-b2) are collinear, then show ...

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