Home
Class 12
MATHS
If x ,y \ a n d \ z are not all zero a...

If `x ,y \ a n d \ z` are not all zero and connected by the equations `a_1x+b_1y+c_1z=0,a_2x+b_2y+c_2z=0`, and `(p_1+lambdaq_1)x+(p_2+lambdaq_2)+(p_3+lambdaq_3)z=0` , show that `lambda=-|[a_1,b_1,c_1],[a_2,b_2,c_2],[p_1,p_2,p_3]|-:|[a_1,b_1,c_1],[a_2,b_2,c_2],[q_1,q_2,q_3]|`

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 a_1x^3 + b_1x² + c_1x + d_1 = 0 and a_2x^3 + b_2x^2+ c_2x + d_2 = 0 have a pair of repeated common roots, then prove that |[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.

the diagonals of the parallelogram formed by the the lines a_1x+b_1y+c_1=0 ,a_1x+b_1y+c_1 '=0 , a_2x+b_2y+c_1=0 , a_2x+b_2y+c_1 =0 will be right angles if:

If x ,y , and z are in G.P. and x+3,y+3 , and z+3 are in H.P., then a. y=2 b. y=3 c. y=1 d. y=0

If the lines a_1x+b_1y+1=0,a_2x+b_2y+1=0 and a_3x+b_3y+1=0 are concurrent, show that the point (a_1, b_1),(a_1, b_2) and (a_3, b_3) are collinear.

Statement 1: If b c+q r=c a+r p=a b+p q=-1, then |ap a p bq b q cr c r|=0(a b c ,p q r!=0)dot Statement 2: if system of equations a_1x+b_1y+c_1=0,a_2x+b_2y+c_2=0,a_3x+b_3y+c_3=0 has non -trivial solutions |a_1b_1c_1 a_2b_2c_2 a_3b_3c_3|=0

Show that the condition for the lines x= a_1z+b_1,y = c_1z+d_1 and x = a_2z+b_2, y = c_2z+ d_2 be perpendicular is a_1a_2+c_1c_2=0

If the points ( a_1,b_1),(a_2,b_2) and (a_1+a_2,b_1+b_2) are collinear ,show that a_1b_2=a_2b_1 .

If the two lines a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 cut the co-ordinates axes in concyclic points. Prove that a_1a_2 = b_1b_2

Represent the following equations in matrix form: a_(1)x+b_(1)y+c_(1)z=k_(1) a_(2)x+b_(2)y+c_(2)z=k_(2) a_(3)x+b_(3)y+c_(3)z=k_(3)

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If [] denotes the greatest integer less than or equal to the real numb...

    Text Solution

    |

  2. If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation...

    Text Solution

    |

  3. If x ,y \ a n d \ z are not all zero and connected by the equations ...

    Text Solution

    |

  4. Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-...

    Text Solution

    |

  5. If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2...

    Text Solution

    |

  6. For what values of k , the following system of equations possesses a...

    Text Solution

    |

  7. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

    Text Solution

    |

  8. Solve for x by Cramers rule x+y+z=6, x-y+z=2 3x+2y-4z=-5

    Text Solution

    |

  9. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

    Text Solution

    |

  10. Find the value of a \ a n d \ b if the system of equation a^2x-b y=a...

    Text Solution

    |

  11. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

    Text Solution

    |

  12. f(x)=|[cosx,x,1],[2sinx,x^2,2x],[tanx,x,1]| . Then value of lim(x->0)(...

    Text Solution

    |

  13. If a system of three linear equations x+4a y+a=0,x+3b y+b=0, and x+2c...

    Text Solution

    |

  14. Let alpha be a repeated root of a quadratic equation f(x)=0 and A(x...

    Text Solution

    |

  15. If |[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+a...

    Text Solution

    |

  16. Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2)),(1+x(2),,1+x(2)x,,1+x(2)x^(...

    Text Solution

    |

  17. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

    Text Solution

    |

  18. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

    Text Solution

    |

  19. Prove that the value of each the following determinants is zero: |a...

    Text Solution

    |

  20. If l1^2+m1^2+n1^2=1 etc., and l1 l2+m1 m2+n1 n2 = 0, etc. and Delta...

    Text Solution

    |