Home
Class 12
MATHS
Without expanding the determinant prove ...

Without expanding the determinant prove that: `{:|(0,p-q,p-r),( q-p,0, q-r),(r-p,r-q,0)|:}=0`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}|=2|{:(a,p,x),(b,q,y),(c,r,z):}|

Given that q^2-p r 0, then the value of {:|(p, q, px+qy), (q, r, qx+ry), (px+qy, qx+ry, 0) |:} is- a. zero b. positive c. negative \ d. q^2+p r

If p + q + r = a + b + c = 0 , then the determinant |{:(pa,qb,rc),(qc,ra,pb),(rb,pc,qa):}| equals

Find the vector perpendicular to the plne determined by the points P(1,-2,2), Q(2,0,-1 ) and R(0,2,1)

If pth,qth and rth terms of an A.P. are a, b, c respectively, then show that a(q-r)+b(r-p)+c(p-q)=0

If p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then |{:(loga,p,1),(logb,q,1),(logc,r,1):}|=0

Sum of the first p,q and r terms of an A.P. are a, b and c, respectively. Prove that, (a)/(p) (q-r) + (b)/(q) (r-p) + (c )/(r ) (p-q) = 0

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

The sum of first p,q and r terms of an AP are a,b and c respectively . Show that (a)/p(q-r)+b/q(r-p)+c/r(p-q)=0

The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q-r) a+(r-p) b+(p-q)c = 0

ALLEN -DETERMINANTS-All Questions
  1. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

    Text Solution

    |

  2. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

    Text Solution

    |

  3. Without expanding the determinant prove that: {:|(0,p-q,p-r),( q-p,0, ...

    Text Solution

    |

  4. Without expanding the determinant prove that: {:|(0,a,-b),(-a,0,-c),(...

    Text Solution

    |

  5. Prove that: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]|=|[a,b,c],[x,y,z],[yz,...

    Text Solution

    |

  6. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

    Text Solution

    |

  7. Prove that: {:|(a^2+2a,2a+1,1), (2a+1,a+2,1),(3,3,1)|:}=(a-1)^3 .

    Text Solution

    |

  8. Using properties of determinants or otherwise evaluate {:|(18, 40, 8...

    Text Solution

    |

  9. Using the property of determinants andd without expanding in following...

    Text Solution

    |

  10. Using the properties of determinants, prove the following |{:(a,b-c,...

    Text Solution

    |

  11. Absolute value of sum of roots of the equation {:|(x+2,2x+3,3x+4), (2x...

    Text Solution

    |

  12. If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the val...

    Text Solution

    |

  13. Suppose three digit numbers A28 , 3B9 and 52C , where A,B and C are in...

    Text Solution

    |

  14. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

    Text Solution

    |

  15. If Dr=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then p...

    Text Solution

    |

  16. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

    Text Solution

    |

  17. Solve the following sets of equations using Cramer's rule and remark a...

    Text Solution

    |

  18. Solve the following sets of equation using Cramers rule and remark ...

    Text Solution

    |

  19. Solve the following sets of equation using Cramers rule and remark ...

    Text Solution

    |

  20. Solve the following sets of equation using Cramers rule and remark ...

    Text Solution

    |