Home
Class 12
MATHS
Let a, b, and c be three real numbers sa...

Let a, b, and c be three real numbers satifying `[(a, b, c)]`
`[(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)]`
If the point P(a, b, c) with reference to (E) lies on the plane `2x+y+z=1`, then the value of `7a+b+c` is

A

0

B

12

C

7

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`a+ 8b +7c = 0, 9a + 2b 3c=0`
`7a + 7b +7c=0`
Solving these equations, we get
`b=6a`
`rArr c= -7a`
Now, `2x + y + z = 0`
`rArr 2a + 6 a + (-7a) = 1`
`rArr a= 1, b = 6, c=-7`
`therefore 7a + b+ c= + 6 - = 6`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|14 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)] Let omega be a solution of x^(3)-1=0 with Im (omega) gt 0 . If a=2 with b and c satisfying (E), then the value of 3/omega^(a)+1/omega^(b)+3/omega^(c) is equal to

Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)] Let b=6 , with a and c satisfying (E). If alpha and beta are the roots of the quadratic equation ax^(2)+bx+c=0 , then sum_(n=0)^(oo) (1/alpha+1/beta)^(n) is

Let P(a, b, c) be any on the plane 3x+2y+z=7 , then find the least value of 2(a^2+b^2+c^2) .

If A = [(2,7),(9,8)] and B = [(1,2),(0,3)] , then find: (A-B).

If A = {:[(4,2,3),(1,5,7)] and B = [(1,3,7),(0,4,1)] , find 2A + B.

If [(a, 3a-b), (2a + c, 3b -d)] = [ (3,2), (4,7)] , find a, b, c and d.

Show that the points A(1,2),B(-1,-16) and C(0,-7) lie on the graph of the linear equation y=9x-7 .

P is a point (a, b, c). Let A, B, C be images of P in y-z, z-x and x-y planes respectively, then the equation of the plane ABC is

Let A = [(1,-2,3), (0,4,7)] and B = [(0,4,2),(2,-2,1)] verify that (A + B)^t = A ^t + B^t

Consider the matrices A = [(1,0,2),(0,2,3)] and B = [(3,5,0,7), (0, -1, 8 ,1)] Find the sum of A and B.

ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let a be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I ...

    Text Solution

    |

  2. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

    Text Solution

    |

  3. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  4. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  5. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

    Text Solution

    |

  6. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  7. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  8. Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) a...

    Text Solution

    |

  9. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

    Text Solution

    |

  10. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  11. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

    Text Solution

    |

  12. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

    Text Solution

    |

  13. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

    Text Solution

    |

  14. IF P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of 3xx3 matrix A and...

    Text Solution

    |

  15. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

    Text Solution

    |

  16. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  17. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

    Text Solution

    |

  18. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

    Text Solution

    |

  19. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

    Text Solution

    |

  20. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisying the equation A A...

    Text Solution

    |