Home
Class 12
MATHS
If the matrix ((a,2/3,2/3),(2/3,1/3,b),(...

If the matrix `((a,2/3,2/3),(2/3,1/3,b),(c,x,y))` is an orthogonal matrix, then `3a-6b=`

Text Solution

Verified by Experts

The correct Answer is:
`5.00`
Promotional Banner

Topper's Solved these Questions

  • NTA TPC JEE MAIN TEST 59

    NTA MOCK TESTS|Exercise MATHEMATICS|30 Videos

  • NTA TPC JEE MAIN TEST 62

    NTA MOCK TESTS|Exercise MATHEMATICS |30 Videos

Similar Questions

Explore conceptually related problems

If A=1/3{:[(1,2,2),(2,1,-2),(a,2,b)]:} is an orthogonal matrix, then

Assertion (A) : If the matrix P = [(0,2b,-2),(3,1,3),(3a,3,3)] is a symmetric matrix, then a = (-2)/(3) and b = (3)/(2) Reason (R) : If P is a symmetric matric, then p' = - p

Show the A=(1)/(3)[(-1,2,-2),(-2,1,2),(2,2,1)] is proper orthogonal matrix.

If the matrix P = [(7,a,4),(-1,3,b),(c, 6, 2)] is a symmetric matrix then the respective values of a ,b,c are

A square matrix A is said to be orthogonal if A^T A=I If A is a square matrix of order n and k is a scalar, then |kA|=K^n |A| . Also |A^T|=|A| and for any two square matrix A and B of same order \|AB|=|A||B| On the basis of above information answer the following question: If A=[(p,q,r),(q,r,p),(r,p,q)] be an orthogonal matrix and pqr=1, then p^3+q^3+r^3 may be equal to (A) 2 (B) 1 (C) 3 (D) -1

Show that the matrix [{:( 1,1,3),( 5,2,6),( -2,-1,-3):}] is nilpotent matrix of index 3.

If matrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is skew-symmetric matrix, then find the values of a,b and c,

If the rank of the matrix A= [(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha)] is 3 then a= (A) -5 (B) 5 (C) 4 (D) 4

NTA MOCK TESTS-NTA TPC JEE MAIN TEST 60-MATHEMATICS
  1. If y(t) satisfies the differential equation y'(t)+2y(t)=2e^(-2t),y(0)=...

    Text Solution

    |

  2. int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AA x gt0 is equal to (c is the cons...

    Text Solution

    |

  3. Find the negation of th statement No square of real number is less tha...

    Text Solution

    |

  4. If the median and the range of four numbers {x,y,2x+y,x-y}, there 0lty...

    Text Solution

    |

  5. If two vertical poles 20m and 80m high stand apart on a horizontal pla...

    Text Solution

    |

  6. The value of tan^(-1)(9/19)+tan^(-1)(9/49)+tan^(-1)(9/97)+tan^(-1)(9/1...

    Text Solution

    |

  7. ("cot"^(2)(pi)/6+"cosec"(5pi)/6+3"tan"^(2)(7pi)/6)/(2"cos"^(2)(pi)/3+"...

    Text Solution

    |

  8. If 0 le x le pi and 16^(sin^(2)x+16^(cos^(2)x)=10, then number of solu...

    Text Solution

    |

  9. If the number of points of discontinuity and number of points of non d...

    Text Solution

    |

  10. A dice is constructed such that probability of occurrence of a number ...

    Text Solution

    |

  11. If P is the coefficient of x^(8) in the expansion of (1+x+x^(2)+x^(3)+...

    Text Solution

    |

  12. If the matrix ((a,2/3,2/3),(2/3,1/3,b),(c,x,y)) is an orthogonal matri...

    Text Solution

    |

  13. The number of wards can be formed with the letters of the word PATALIP...

    Text Solution

    |

  14. If the roots of 7x^(2)-15x+alpha=0 are rational numbers, then the numb...

    Text Solution

    |

  15. Let C(1):4(x-4)^(2)+25y^(2)-100=0 and C(2):4(x+1)^(2)+y^(2)-4=0 be con...

    Text Solution

    |

  16. Find the number of common tangents to the circles x^(2)+y^(2)-4x-6y-12...

    Text Solution

    |

  17. Let O be any point inside a tetrahedron ABCD. The line joining O to t...

    Text Solution

    |

  18. If [.] represents the greatest integer function where f(x)=cos[pi^(2...

    Text Solution

    |

  19. If int(0)^(oo)(sinx)/x dx=A and F(t)=int(0)^(oo)(1-cos(tx))/(x^(2))dx,...

    Text Solution

    |

  20. let f(x)=sum(k=0)^(8)A(k)x^(k). If f(x)+f(omega x)+f(omega^(2)x), wher...

    Text Solution

    |