Home
Class 12
MATHS
Let A,B,C are 3 points on the complex pl...

Let `A,B,C` are `3` points on the complex plane represented by complex number `a,b,c` respectively such that `|a|= |b|= |c|=1,a+b+c = abc=1`, then

A

area of triangle `ABC` is `2` (square unit)

B

triangle `ABC` is an equilateral triangle

C

traingle `ABC` is right isosceles triangle.

D

orthocentre of traingle `ABC` lies outside the triangle

Text Solution

Verified by Experts

The correct Answer is:
C
`bar(a)+bar(b)+bar(c )=1`
`implies ab+bc+ca = 1`
implies a,b,c are roots of cubic
`z^(3)-z^(2)+z-1=0`
`(z^(2)+1)(z-1)=0`
`implies z=pm i,1`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    ALLEN |Exercise part-2 Mathematics|15 Videos

  • TEST PAPERS

    ALLEN |Exercise part-2 Mathematic|17 Videos

  • TEST PAPER

    ALLEN |Exercise CHEMISTRY SECTION-II|16 Videos

  • VECTOR ALGEBRA

    ALLEN |Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

The points A,B and C represent the complex numbers z_(1),z_(2),(1-i)z_(1)+iz_(2) respectively, on the complex plane (where, i=sqrt(-1) ). The /_\ABC , is

The points A,B,C represent the complex numbers z_1,z_2,z_3 respectively on a complex plane & the angle B & C of the triangle ABC are each equal to 1/2 (pi-alpha) . If (z_2-z_3)^2=lambda(z_3-z_1)(z_1-z_2) (sin^2) alpha/2 then determine lambda .

Consider a Delta ABC and let a,b, and c denote the leghts of the sides opposite to vertices A,B and C, respectively. Suppose a=2,b =3, c=4 and H be the orthocentre. Find 15(HA)^(2).

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that AD,BE and CF are concurrent, then show that (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

A,B and C are the points respectively the complex numbers z_(1),z_(2) and z_(3) respectivley, on the complex plane and the circumcentre of /_\ABC lies at the origin. If the altitude of the triangle through the vertex. A meets the circumcircle again at P, prove that P represents the complex number (-(z_(2)z_(3))/(z_(1))) .

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

Consider a DeltaABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C, repectively. if a=1,b=3 and C=60^(@), then sin ^(2) B is equal to

Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numbers such that a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z .Then, the value of (|x|^2+|y|^2|+|z|^2)/(|a|^2+|b|^2+|c|^2)

If the percentage errors of A,B,and C are a, b, and c, respectively ,then the total percentage error in the product ABC is

Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a', b', c', respectively from the origin, then prove that (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/((a')^2)+(1)/((b')^2)+(1)/((c')^2) .

ALLEN -TEST PAPERS-MATHEMATICS
  1. Let A,B,C are 3 points on the complex plane represented by complex num...

    Text Solution

    |

  2. If a be sum of the odd numbered terms and b the sum of even numbered ...

    Text Solution

    |

  3. In the expansion of (2x-(x^(2))/4)^(9) the sum of two middle terms is

    Text Solution

    |

  4. Number of rational terms in the expansion of (sqrt(2)+root(4)(3))^(100...

    Text Solution

    |

  5. In the expansion of ((x+1)/(x^(2//3)-x^(1//3)+1)-(x-1)/(x-x^(1//2)))^(...

    Text Solution

    |

  6. Value of a if 17th and 18 th terms in the expansion of (2+a)^(50) are ...

    Text Solution

    |

  7. In the expansion of (x^2+2x+2)^n, nepsilonN (A) coefficient of x=n.2^n...

    Text Solution

    |

  8. If the coefficients of first three terms in the expansion of (sqrt(x)+...

    Text Solution

    |

  9. the possible value(s) of positive integer n for which 4^(n)+1 is divis...

    Text Solution

    |

  10. Which of the following is/are true

    Text Solution

    |

  11. Value of .^(n)C(0)^(2)+3.^(n)C(1)^(2)+5.^(n)C(2)^(2)………….. upto (n+1) ...

    Text Solution

    |

  12. Consider expansion of (1+x)^(200)=a(0)+a(1)x+a(2)x^(2)+………+a(200)x^(20...

    Text Solution

    |

  13. Consider expansion of (1+x)^(200)=a(0)+a(1)x+a(2)x^(2)+………+a(200)x^(20...

    Text Solution

    |

  14. Consider (1+x)^(n+1)=A(0)+A(1)x+A(2)x^(2)+………………+A(n+1)x^(n+1) and a...

    Text Solution

    |

  15. Consider (1+x)^(n+1)=A(0)+A(1)x+A(2)x^(2)+………………+A(n+1)x^(n+1) and a...

    Text Solution

    |

  16. If (1+x-3x^2)^2145 = a0+a1 x+a2 x^2+... then a0-a1+a2-.. ends with

    Text Solution

    |

  17. Sum of all the digits of the coefficient of x^(5) in the expansion of ...

    Text Solution

    |

  18. If the ratio of the coefficient of x^(10) in (1-x^(2))^(10) and term i...

    Text Solution

    |

  19. If the sum sum(k=1)^(2008)k.^(2008)C(k) can be expressed as 2^(m)I whe...

    Text Solution

    |

  20. In the expansion of (5^(1//2)+7^(1//8))^(1024) if the number of integr...

    Text Solution

    |

  21. If sum(r=0)^(10)r.^(10)C(x).3^(4).(-2)^(10-r)=S, then S/10 is equal to

    Text Solution

    |