Home
Class 11
MATHS
If a ,b ,c and u ,v ,w are the complex n...

If `a ,b ,c` and `u ,v ,w` are the complex numbers representing the vertices of two triangles such that `(c=(1-r)a+r b` and `w=(1-r)u+r v ,` where `r` is a complex number, then the two triangles (a)have the same area (b) are similar (c)are congruent (d) None of these

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

The radii r_(1), r_(2), r_(3) of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24 cm^(2) and its perimeter is 24 cm, then the length of its largest side is (a) 10 (b) 9 (c) 8 (d) none of these

In triangle ABC, if A - B = 120 and R = 8r , where R and r have their usual meaning, then cos C equals

If t and c are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t+b)/(t-c), z=x+i ydot Locus of z is (where a, b are complex numbers) a. line segment b. straight line c. circle d. none of these

If a ,b ,c in R , then find the number of real roots of the equation Delta =|[x, c,-b],[-c, x, a], [b,-a,x]|=0

If x in R ,a n da ,b ,c are in ascending or descending order of magnitude, show that (x-a)(x-c)//(x-b)(w h e r ex!=b) can assume any real value.

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to a+b (b) b+c c+a (d) a+b+c

The position vectors of the vertices A ,B ,a n dC of a triangle are hat i+ hat j , hat j+ hat ka n d hat i+ hat k , respectively. Find the unit vector hat r lying in the plane of A B C and perpendicular to I A ,w h e r eI is the incentre of the triangle.

In DeltaABC, R, r, r_(1), r_(2), r_(3) denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that r_(1) :r_(2): r_(3) = 1: 2 : 3 The sides of the triangle are in the ratio

For the sequence {u_(n)} if u_(1) - 2 and u_(r+1) = u_(r) +r+2 , for all natural number r, find the 10th term of the sequence.

If z=omega,omega^2 where omega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex may be represented by a, z=1 b. z=0 c. z=-2 d. z=-1

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z1a n dz2 are two nonzero complex numbers such that =|z1+z2|=|z1|+|...

    Text Solution

    |

  2. If diagonals of a parallelogram bisect each other, prove that its a rh...

    Text Solution

    |

  3. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

    Text Solution

    |

  4. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

    Text Solution

    |

  5. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

    Text Solution

    |

  6. If z=x+iy is a complex number with x, y in Q and |z| = 1, then show ...

    Text Solution

    |

  7. Referred to the principal axes as the axes of co ordinates find the eq...

    Text Solution

    |

  8. Find the area bounded by |arg z|lt=pi//4 and |z-1|<|z-3|dot

    Text Solution

    |

  9. Find sum(k=1)^6 (sin,(2pik)/7 -icos, (2pik)/7)=?

    Text Solution

    |

  10. If the equation a x^2+b x+c=0(a &gt;0) has two real roots alphaa n db...

    Text Solution

    |

  11. If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c<...

    Text Solution

    |

  12. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

    Text Solution

    |

  13. Let z=x+i y be a complex number, where xa n dy are real numbers. Let...

    Text Solution

    |

  14. If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5 , then prove that I m(z)=...

    Text Solution

    |

  15. The value of sum(n=1)^(13) (i^n+i^(n+1)), where i =sqrt(-1) equals ...

    Text Solution

    |

  16. If c!=0 and the equation p//(2x)=a//(x+c)+b//(x-c) has two equal roots...

    Text Solution

    |

  17. If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a r...

    Text Solution

    |

  18. Express the following in a+i b form: ((cos2theta-isin2theta)^4(cos4...

    Text Solution

    |

  19. The roots of the equation t^3+3a t^2+3b t+c=0a r ez1, z2, z3 which rep...

    Text Solution

    |

  20. Solve the equation (x-1)^3+8=0 in the set C of all complex numbers.

    Text Solution

    |