Home
Class 12
MATHS
if (x(1),x(2))^(2)+(y(1)-y(2))^(2)=a^(2)...

if `(x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2).` where a,b,c are positive then prove that `4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a)
(c+a-b)(a+b-c)`

Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise PART-II:|28 Videos

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

If (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2)(x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2)(x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2) and 2s=a+b+c then (1)/(4)det[[x_(2),y_(2),1x_(3),y_(3),1]]^(2)

If (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=144,(x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=25 and (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=169, then the value of det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2) is 30(b)30^(2)(c)60(d)60^(2)

The centroid of the triangle with vertices at A(x_(1),y_(1)),B(x_(2),y_(2)),c(x_(3),y_(3)) is

The centroid of the triangle formed by A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) is

If (x_1-x_2)^2+(y_1-y_2)^2=a^2,(x_2-x_3)^2+(y_2-y_3)^2=b^2 and (x_3-x_1)^2+(y_3-y_1)^2=c^2 then prove that 4|{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}|= (a+b+c)(b+c-a)(c+a-b)(a+b-c)

If A (x_(1), y_(1)), B (x_(2), y_(2)) and C (x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)| is equal to

The area of the Quadrilateral with vertices A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) and D(x_(4),y_(4)) is

RESONANCE-MATRICES & DETERMINANT-HLP
  1. Prove that Delta=|{:(,beta(gamma),beta(gamma)'+beta'(gamma),beta'(gamm...

    Text Solution

    |

  2. If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...

    Text Solution

    |

  3. if (x(1),x(2))^(2)+(y(1)-y(2))^(2)=a^(2), (x(2)-x(3))^(2)+(y(2)-y(3))^...

    Text Solution

    |

  4. Let A=[(cos^(- 1)x,cos^(- 1)y,cos^(- 1)z),(cos^(- 1)y,cos^(- 1)z,cos^...

    Text Solution

    |

  5. If y=(u)/(v), where u and v are functions of x, show that v^(3)(d^(2...

    Text Solution

    |

  6. If alpha&beta be the real roots of ax^(2)+bx+c=0 and s(n)=alpha^(n)+be...

    Text Solution

    |

  7. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |

  8. Let overset(to)(a(r))=x(r )hat(i)+y(r )hat(j)+z(r )hat(k),r=1,2,3 thre...

    Text Solution

    |

  9. If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3)...

    Text Solution

    |

  10. If the determinant |(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h)| splits ...

    Text Solution

    |

  11. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

    Text Solution

    |

  12. If a,b,c are comples number and z=|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c...

    Text Solution

    |

  13. If f(x)=log(10)x and g(x)=e^(ln x) and h(x)=f [g(x)], then find the va...

    Text Solution

    |

  14. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

    Text Solution

    |

  15. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

    Text Solution

    |

  16. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

    Text Solution

    |

  17. Let 'A' is (4xx4) matrix such that the sum of elements in each row is ...

    Text Solution

    |

  18. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

    Text Solution

    |

  19. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

    Text Solution

    |

  20. Let p and q be real number such that x^(2)+px+q ne0 for every real num...

    Text Solution

    |