Home
Class 12
MATHS
Let veca,vecb and vecc be three non-copl...

Let `veca,vecb and vecc` be three non-coplanar unit vectors such that the angle bet ween every pair of them is `pi/3`. If `vecaxxvecb+vecbxxvecc=pveca+qvecb+rvecc`, where p,q and r are scalars, then the value of `frac{p^2+2q^2+r^2}{q^2}` is :

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos
  • INTEGRALS

    MODERN PUBLICATION|Exercise EXERCISE|768 Videos

Similar Questions

Explore conceptually related problems

If veca,vecb and vecc are three unit vectors such that veca*vecb=veca*vecc=0 and angle between vecb and vecc is pi/6 , prove that veca=+-2(vecb xxvecc) .

If veca,vecb and vecc are non coplanar and unit vectors such that vecaxx(vecbxxvecc)=(vecb+vecc)/sqrt2 then the angle between veca and vecb is

Let veca,vecb and vecc be three non-zero vectors such that no two of them are collinear and (vecaxxvecb)xxvecc=1/3|vecb||vecc|veca . If 'theta' is the angle between the vectors vecb and vecc , then a value of sin theta is :

If veca, vecb and vecc are non-coplanar vectors, prove that the four points 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+ 6 vecc are coplanar.

If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(veccxxvecd)=1 and veca.vecc=1/2, then

Let veca,vecb and vecc be three unit vectors such that : vecaxx(vecbxxvecc)=(sqrt3)/2 (vecb+vecc) . If vecb is not parallel to vecc , then angle between veca and vecb is :

If vecb and vecc are two non-collinear such that veca ||(vecbxxvecc) . Then prove that (vecaxxvecb).(vecaxxvecc) is equal to |veca|^(2)(vecb.vecc)

If veca, vecb and vecc are non-coplanar vectors and lamda is a real number, then the vectors veca + 2vecb + 3vecc, lamda vecb + mu vecc and (2lamda -1)vecc are coplanar when

If veca,vecb,vecc are three non-zero vectors such that each one of these is perpendicular to the sum of the other two vectors, then the value of |veca+vecb+vecc|^2 is :

If veca, vecb, vecc are non coplanar vectors and lamda is a real number, then [(lamda(veca+vecb), lamda^(2)vecb, lamdavecc)]=[(veca, vecb+vecc,vecb)] for

MODERN PUBLICATION-EXCLUSIVELY FOR JEE(ADVANCED)-EXERCISE
  1. If A and B are two events such that P(B)ne1, B^c denotes the event com...

    Text Solution

    |

  2. Suppose that vecp, vecq and vecr are three non-coplanar vectors in R^3...

    Text Solution

    |

  3. Let veca,vecb and vecc be three non-coplanar unit vectors such that th...

    Text Solution

    |

  4. The square of the shortest distance between the lines : vecr=s(hati-ha...

    Text Solution

    |

  5. Write the set A={x:x is an integer,−1≤x≤4} in roster form.

    Text Solution

    |

  6. If |veca|=3, |vecb|=1 and |veca+vecb|=|veca-vecb|, then |veca xx vecb|...

    Text Solution

    |

  7. If |veca|=|vecb|=|vecc|=1 and veca*vecb=vecb*vecc=vecc*veca=1/2, then ...

    Text Solution

    |

  8. Consider the lines : L1: (x-7)/3=(y-7)/2=(z-3)/1 and L2: (x-1)/2=(y+1)...

    Text Solution

    |

  9. Value of lambda so that the planes: x-y+z+1=0, lambdax+3y+2z-3=0, 3x+l...

    Text Solution

    |

  10. If A and B are two events of an expeiment with P(A)=1/4, P(AuuB)=1/2, ...

    Text Solution

    |

  11. One function is selected at random from all functions of the set S={1,...

    Text Solution

    |

  12. Football teams T1 and T2 have to play two games against each other. It...

    Text Solution

    |

  13. Football teams T1 and T2 have to play two games against each other. It...

    Text Solution

    |

  14. Find the S.D. between the lines : (x-3)/3=(y-8)/-1=(z-3)/1 and (x+3)/-...

    Text Solution

    |

  15. Find the S.D. between the lines : (x-3)/3=(y-8)/-1=(z-3)/1 and (x+3)/-...

    Text Solution

    |

  16. Box 1 contains three cards bearing number 1,2,3 , box 2 contains five ...

    Text Solution

    |

  17. Box 1 contains three cards bearing number 1,2,3 , box 2 contains five ...

    Text Solution

    |

  18. A fair die is tossed repeated until a six is obtained. Let X denote th...

    Text Solution

    |

  19. A fair die is tossed repeatedly until a 6 is obtained. Let X denote th...

    Text Solution

    |

  20. Let n1 and n2 be the number of red and black balls respectively, in bo...

    Text Solution

    |