Home
Class 12
MATHS
Let Delta1=|{:(a1,a2,a3),(b1,b2,b3),(c1,...

Let `Delta_1=|{:(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3):}| , Delta_2=|{:(6a_1,2a_2,2a_3),(3b_1,b_2,b_3),(12c_1, 4c_2,4c_3):}|` and `Delta_3=|{:(3a_1+b_1 , 3a_2+b_2 , 3a_3+b_3),(3b_1,3b_2,3b_3),(3c_1,3c_2,3c_3):}|`
then `Delta_3-Delta_2=kDelta_1`, find k.

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

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| and Delta_1=|(a_1+pb_1,b_1+qc_1,c_1+ra_1),(a_2+pb_2,b_2+qc_2,c _2+ra_2),(a_3+pb_3,b_3+qc_3,c_3+ra_3)| then Delta_1=

Find the value of lambda for which |{:(2a_1+b_1 , 2a_2+b_2 , 2a_3+b_3),(2b_1+c_1, 2b_2+c_2 , 2b_3+c_3),(2c_1+a_1,2c_2+a_2, 2c_3+a_3):}|=lambda|{:(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3):}|

|{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

If D= |{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| and A_1,B_1,C_1 etc. are the respective cofactors of the elements a_1,b_1,c_1 etc. then D will be-

Evaluate : |{:(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}|

A={a,b,c} and B={1,2,3} are two sets R={(a,1),(a,2),(b,2),(b,3),(c,1)} be a subset of AxxB then R is a

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by a. a+b b. a+2b c. 2a+3b d. a^2

prove that , |{:(1,1+a,1+a+b),(2,3+2a,4+3a+2b),(3,6+3a,10+6a+3b):}|=1

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​is ...

    Text Solution

    |

  2. Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...

    Text Solution

    |

  3. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  4. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

    Text Solution

    |

  5. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

    Text Solution

    |

  6. The product of all values of t , for which the system of equations (a-...

    Text Solution

    |

  7. "If " a(1) ,a(2), a(3)….." are in A.P, then find the value of the fol...

    Text Solution

    |

  8. Let omega=-1/2+i(sqrt(3))/2. Then the value of the determinant |(1,1,1...

    Text Solution

    |

  9. Factorize: a x+b x+a y+b y +a x^2+b y^2+b x^2+a y^2 a^2+b c+a b+...

    Text Solution

    |

  10. If g(x)=|[a^(-x),e^(x loge a),x^2],[a^(-3x),e^(3x loge a),x^4],[a^(-5x...

    Text Solution

    |

  11. The sum of values of p for which the equations x+y+z=1, x+2y +4z...

    Text Solution

    |

  12. The value of |alpha| for which the system of equation alphax+y+z=...

    Text Solution

    |

  13. Let D1=|[a, b, a+b], [c, d, c+d], [a, b, a-b]| and D2=|[a, c, a+c], [b...

    Text Solution

    |

  14. Three distinct points P(3u^(2),2u^(3));Q(3v^(2),2v^(3)) and R(3w^(2),2...

    Text Solution

    |

  15. If |[x,x+y, x+y+z],[2x,3x+2y,4x+3y+2z],[3x,6x+3y, 10 x+6y+3z]|=64 , th...

    Text Solution

    |

  16. Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) ...

    Text Solution

    |

  17. If |[x^n,x^(n+2),x^(n+4)],[y^n,y^(n+2),y^(n+4)],[z^n, z^(n+2),z^(n+4)]...

    Text Solution

    |

  18. Let Delta1=|{:(a1,a2,a3),(b1,b2,b3),(c1,c2,c3):}| , Delta2=|{:(6a1,2a2...

    Text Solution

    |

  19. The value of |[2x1y1, x1y2+x2y1, x1y3+x3y1], [x1y2+x2y1, 2x2y2, x2y3+...

    Text Solution

    |

  20. Given A=|[a,b,2c],[d,e,2f],[l,m,2n]|,B=|[f,2d,e],[2n,4l,2m],[c,2a,b]| ...

    Text Solution

    |