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An equilateral triangle has each side to a. If the coordinates of its vertices are `(x_(1), y_(1)), (x_(2), y_(2))` and `(x_(3), y_(2))` and `(x_(3), y_(3))` then the square of the determinat `|(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|` equals

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An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

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If x_(1),x_(2),x_(3) and y_(1),y_(2),y_(3) are both in G.P. with the same common ratio then the points (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3))

MODERN PUBLICATION-DETERMINANTS-Exercise 4(d) (LONG ANSWER TYPE QUESTIONS)
  1. Find the area of the triangle with vertices at the points given in eac...

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  2. Using determinants , show that the following points are collinear : ...

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  3. Use determinants to show that the following points are collinear. (i...

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  4. If the points (3, -2), (x ,\ 2) and (8 ,8) are collinear, find x us...

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  5. If the area of triangle is 35sq.units with vertices (2,-6), (5,4) and ...

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  6. If area of DeltaABC is 12 square units and vertices are A(x,2), B(4,-1...

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  7. Find the values of 'k' if area of the triangle is 4 square unts and ve...

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  8. Find the values of k if area of triangle is 4 sq. units and vertices a...

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

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  10. Find the equation of the line joining the following points, using dete...

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  11. (i) Find the equation of line joining (1,2) and (3,4) using determinan...

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

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  13. Prove that the area of the triangle whose vertices are : (at(1)^(2),...

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  14. Show that pointsA (a , b + c), B (b , c + a), C (c , a + b)are collin...

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  15. If the points (a(1),b(1))m(a(2),b(2))" and " (a(1)-a(2),b(2)-b(2)) are...

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  16. If P(x , y) is any point on the line joining the point A(a ,0)a n dB(0...

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  17. An equilateral triangle has each side to a. If the coordinates of its ...

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