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If the co-ordinates of the vertices of a...

If the co-ordinates of the vertices of an equilateral trianlg with sides of length 'a' are `(x_1,y_1),(x_2,y_2),(x_3,y_3)`, then Prove that
`|{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}|^2=(3/4)a^4.`

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The correct Answer is:
`3/4a^4`
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KUMAR PRAKASHAN-DETERMINANTS -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Evaluate the determinants below in examples number 1 and 2 |{:(x^2-x...

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  2. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  3. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  4. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  5. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  6. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

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  7. Using the proprties of determinants in Exercise 7 to 9, prove that |...

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  8. Using the proprties of determinants in Exercise 7 to 9, prove that |...

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  9. Using the proprties of determinants in Exercise 7 to 9, prove that |...

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  10. If A+B+C = 0 then prove that |{:(1,cosC,cosB),(cosC,1,cosA),(cosB,co...

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  11. If the co-ordinates of the vertices of an equilateral trianlg with sid...

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  12. Find the value of theta satisfying |{:(1,1,sin3theta),(-4,3,cos2thet...

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  13. If |{:(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x):}|=0 then find values ...

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  14. If a1,a2,a3….ar are in G.P then show that |{:(a(r+1),a(r+5),a(r+9)),(a...

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  15. Show that the points (a+5,a-4),(a-2,a+3) and (a,a) do not lie on a str...

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  16. Show that the DeltaABC is an isosceles triangle if the determinant D...

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  17. Find A^(-1)" if "A=[{:(0,1,1),(1,0,1),(1,1,0):}] and show that A^(-1)=...

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