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Let A(1, 3), B(0, 0) and C(k, 0) be thre...

Let A(1, 3), B(0, 0) and C(k, 0) be three points such that `ar(triangle ABC) =3` sq units. Find the value of k.

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To find the value of \( k \) such that the area of triangle \( ABC \) is \( 3 \) square units, we can use the formula for the area of a triangle given by the coordinates of its vertices. The vertices are given as: - \( A(1, 3) \) - \( B(0, 0) \) - \( C(k, 0) \) ### Step 1: Area of Triangle Formula The area \( A \) of triangle formed by points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) can be calculated using the determinant formula: ...
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RS AGGARWAL-DETERMINANTS-Objective Questions
  1. Let A(1, 3), B(0, 0) and C(k, 0) be three points such that ar(triangle...

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  2. |["cos"70^(@), "sin"20^(@)], ["sin"70^(@), "cos"20^(@)]|=?

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  3. |["cos"15^(@), "sin"15^(@)], ["sin"15^(@), "cos"15^(@)]|=?

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  4. |["sin"23^(@), -"sin"7^(@)], ["cos"23^(@), "cos"7^(@)]|=?

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  5. Evaluate: |(a+i b, c+i d),(-c+i d, a-i b)|

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  6. Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| ...

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  7. If omega is a complex cube root of unity then the value of the determi...

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  8. If A=[[1^2,2^2,3^2],[2^2,3^2,4^2],[3^2,4^2,5^2]] then |AdjA|=

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  9. |(1!,2!,3!),(2!,3!,4!),(3!,4!,5!)|=?

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  10. |[a-b, b-c, c-a], [b-c, c-a, a-b], [c-a, a-b, b-c]|=?

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  11. find |(1, 1+p,1+p+q),(2, 3+2p,1+3p+2q),(3, 6+3p, 1+6 p+3q)|=.

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  12. |{:(1, 1, 1),(a, b, c),(a^(3), b^(3), c^(3)):}|= is equal to

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  13. Without expanding evaluate the determinant |(sinalpha,cosalpha,sin(alp...

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  14. If a, b, c be distinct positive real numbers then the value of |[a, b,...

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  15. Q. |(x+y,x,x),(15x+4y,4x,2x),(10x +8y,8x,3x)|=x^3

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  16. Evaluate the following: |[a^2+2a, 2a+1, 1],[2a+1, a+2, 1],[3,3,1]|

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  17. |[a, a+2b, a+2b+3c], [3a, 4a+6b, 5a+7b+9c], [6a, 9a+12b, 11a+15b+18c]|...

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  18. Prove that|[b+c,a,b],[c+a,c,a],[a+b,b,c]|=(a+b+c)(a-c)^2

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  19. |[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]|=?

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  20. |[bc, b+c, 1], [ca, c+a, 1], [ab, a+b, 1]|=?

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  21. |[b+c, a, a], [b, c+a, b], [c, c, a+b]|=?

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