Home
Class 12
MATHS
If A , B ,C are angles of a triangle, th...

If `A , B ,C` are angles of a triangle, then the value of `|[e^(2i A),e^(-i C),e^(-i B)],[e^(-i C),e^(2i B),e^(-i A)],[e^(-i B),e^(-i A),e^(2i C)]|` is (a)`1` (b) `-1` (c) `-2` (d) `-4`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e^(-2) (D) 4e^(-2)

If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e^(ipi//4)],[e^(-ipi//3),1,e^(i2pi//3)],[e^(-ipi//4),e^(-i2pi//3),1]|

The value of lim_(x->1)(2-x)^(tan((pix)/2)) is (a) e^(-2/pi) (b) e^(1/pi) (c) e^(2/pi) (d) e^(-1/pi)

If a,b,c,d,e are in A.P., then the value of (a+b+5c-5d+e) in terms of a is-

Prove that , the minimum value of (i) 4e^(2x)+9e^(-2x)" is "12 , (ii) (x)/(logx) is e.

If I_(m)=int_(1)^(e )(log_(e)x)^(m)dx , then the value of (I_(m)+mI_(m-1)) is -

The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 (d) 0

If I=intsec^2xcos e c^4x dx=Acot^3x+Btanx+Ccotx+D , then find the values of A,B,C and D.

If I_(1)=int e^(x) cos x dx and I_(2)=int e^(x) sin x dx , then the value of I_(1)+I_(2) is-

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

    Text Solution

    |

  2. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

    Text Solution

    |

  3. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

    Text Solution

    |

  4. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

    Text Solution

    |

  5. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, a) There are ex...

    Text Solution

    |

  6. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

    Text Solution

    |

  7. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

    Text Solution

    |

  8. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

    Text Solution

    |

  9. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

    Text Solution

    |

  10. If Dk=|[1, n, n];[ 2k, n^2+n+1, n^2+n];[ 2k-1, n^2, n^2+n+1]|a n...

    Text Solution

    |

  11. If p+-a, q+- b, r+-c and abs((p,b,c),(a,q,c),(a,b,r)) = 0 show that p...

    Text Solution

    |

  12. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

    Text Solution

    |

  13. If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...

    Text Solution

    |

  14. For a fixed positive integer n , if Delta=|[n !,(n+1)!,(n+2)!],[(n+1)!...

    Text Solution

    |

  15. The lines 2x-y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

    Text Solution

    |

  16. if f(alpha,beta)=|[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[co...

    Text Solution

    |

  17. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

    Text Solution

    |

  18. If (1+x+x^(2))^(25)=a(0)+a(1)x+a(2)x^(2)+...+a(50).x^(50), then a(0)+a...

    Text Solution

    |

  19. Find the value of lambda for which the homogeneous system of equations...

    Text Solution

    |

  20. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

    Text Solution

    |