Home
Class 11
MATHS
Let vec a = vec i + vec j + vec k and le...

Let `vec a = vec i + vec j + vec k` and let `vec r` be a variable vector such that `vec r cdot vec i , vec r cdot vec j` and `vec r cdot vec k` are positive integers. If `vec r cdot vec a le 12` then the number of values of `vec r` is

A

`.^12C_9` - 1

B

`.^12C_3`

C

`.^12C_9`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • PARABOLA, ELLIPSE AND HYPERBOLA

    PATHFINDER|Exercise QUESTION BANK|66 Videos

  • PERMUTATION AND COMBINATIONS

    PATHFINDER|Exercise QUESTION BANK|81 Videos

Similar Questions

Explore conceptually related problems

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=sqrt3a n d| vec b|=sqrt2. Then vec r =?

Let vec a=- hat i- hat k , vec b=- hat i+ hat ja n d vec c= hat i+2 hat j+3 hat k be three given vectors. If vec r is a vector such that vec rxx vec b= vec cxx vec b and vec r dot vec a=0, then find the value of vec rdot vec bdot

If vec a= hat i+ hat j+ hat k and vec b= hat i-2 hat j+ hat k , then find vector vec c such that vec a . vec c=2 and vec axx vec c= vec bdot

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=4(Area \ of triangle ABC).

If vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec k a n d vec c= vec i+ vec j+ vec k , then find thevalue of ( vec axx vec b)dot(( vec axx vec c)dot)

Let vec r , vec a , vec ba n d vec c be four nonzero vectors such that vec rdot vec a=0,| vec rxx vec b|=| vec r|| vec b|a n d| vec rxx vec c|=| vec r|| vec c|dot Then [abc] is equal to |a||b||c| b. -|a||b||c| c. 0 d. none of these

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

PATHFINDER-PERMUTATION AND COMBINATION-QUESTION BANK
  1. The number of ways in which three numbers in A.P. can be selected from...

    Text Solution

    |

  2. If n lt p lt 2n and p is prime and N = .^(2n)Cn, then

    Text Solution

    |

  3. Let vec a = vec i + vec j + vec k and let vec r be a variable vector s...

    Text Solution

    |

  4. 2^m3^n5^p is a divisor of 2^10 cdot 3^8 cdot 5^7 if m, n and p are all...

    Text Solution

    |

  5. 2^m3^n5^p is a divisor of 2^10 cdot 3^8 cdot 5^7 if m, n and p are all...

    Text Solution

    |

  6. 2^m3^n5^p is a divisor of 2^10 cdot 3^8 cdot 5^7 if m, n and p are all...

    Text Solution

    |

  7. Different words are being formed by arranging the letters of the words...

    Text Solution

    |

  8. Different words are being formed by arranging the letters of the words...

    Text Solution

    |

  9. Different words are being formed by arranging the letters of the words...

    Text Solution

    |

  10. Match List - I with List - II

    Text Solution

    |

  11. Match List - I with List - II

    Text Solution

    |

  12. John has x children by his first wife,. Mary has (k + 1) children by h...

    Text Solution

    |

  13. the remainder obtained 1! + 2! + ......+1200! is divided by 14 is

    Text Solution

    |

  14. A bouquet from 11 different flowers is to be made so that it contains ...

    Text Solution

    |

  15. If .^nPr = .^nP(r + 1) and .^nCr = .^nC(r-1) then the value of n + r...

    Text Solution

    |

  16. A five digit number divisible by 3 is to be formed using the numerals ...

    Text Solution

    |

  17. Find the number of number between 300 and 3000 that can be formed with...

    Text Solution

    |

  18. A number of four different digits is formed with the help of the digit...

    Text Solution

    |

  19. A number of four different digits is formed with the help of the digit...

    Text Solution

    |

  20. A number of four different digits is formed with the help of the digit...

    Text Solution

    |