Home
Class 12
MATHS
Let a=hatj-hatk and c=hati-hatj-hatk, th...

Let `a=hatj-hatk and c=hati-hatj-hatk`, the vector b satisfying `axxb+c=vec0` and a.b=3, is

A

`-hati+hatj-2hatk`

B

`2hati-hatj+2hatk`

C

`hati-hatj-2hatk`

D

`hati+hatj-2hati`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `a xx b + c = 0`
`rArr a xx (a xx b) + a xx c = 0`
`rArr (a.b)a - (a.a) + a xx c = 0`
`rArr 3a - 2b +a xx c = 0`
`rArr 2b = 3a+ a xx c`
`rArr 2b = 3hatj - 3hatk -2hati - hatj - hatk`
`rArr 2b = - hati + 2hatj - 4hatk`
`:. b = - hati + hatj - 2hatk`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise ( MHT CET Corner)|66 Videos

  • VECTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise ( MHT CET Corner)|66 Videos

  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|20 Videos

Similar Questions

Explore conceptually related problems

Let veca=hatj-hatk and vecc=hati-hatj-hatk . Then the vector vecb satisfying vecaxxvecb+vecc=vec0 and veca.vecb=3 is

Let a=hati - hatj, b=hati + hatj + hatk and c be a vector such that a xx c + b=0 and a.c =4, then |c|^(2) is equal to .

Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hatk be three vectors . A vector in the pland of vecb and vecc whose projection on veca is of magnitude sqrt((2/3)) is (A) 2hati+3hatj+3hatk (B) 2hati+3hatj-3hatk (C) -2hati-hatj+5hatk (D) 2hati+hatj+5hatk

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -(VECTORS ) Exercise 2 ( Topical problems )
  1. If the vectors phati+hatj+hatk, hati, qhatj+hatk and hati+hatj+rhatk(p...

    Text Solution

    |

  2. Let a, b and c be three non-zero vectors which are pairwise non-collin...

    Text Solution

    |

  3. Let a=hatj-hatk and c=hati-hatj-hatk, the vector b satisfying axxb+c=v...

    Text Solution

    |

  4. If the vectors a=hati-hatj+2hatk, b=2hati+4hatj+hatk and c=lambdahati+...

    Text Solution

    |

  5. Let a=hati+hatj+hatk, b=hati-hatj+2hatk and c=x hati+(x-2) hatj-hatk. ...

    Text Solution

    |

  6. The value of a, for which the points A, B and C with position vectors ...

    Text Solution

    |

  7. For any vector a, then the value of (axxhati)^(2)+(a xxhatj)^(2)+(a...

    Text Solution

    |

  8. If a=hati-hatk, b=xhati+hatj=(1-x)hatk and c=yhati+xhatj+(1+x-y)hatk. ...

    Text Solution

    |

  9. Let a, b and c be distinct non-negative numbers. If the vectors ahati+...

    Text Solution

    |

  10. If a, b, c are non-coplanar vectors and lambda is a real number, then ...

    Text Solution

    |

  11. Let a, b and c be three non-zero vectors such that no two of these are...

    Text Solution

    |

  12. A particle is acted upon by constant forces 4hati+hatj-3hatk and 3hati...

    Text Solution

    |

  13. Let u, v and w be such that |u|=1, |v|=2, |w|=3 If the projection ...

    Text Solution

    |

  14. The value of [(a-b)(b-c)(c-a)] is equal to

    Text Solution

    |

  15. If hat(i)+hat(j), hat(j)+hat(k), hat(i)+hat(k) are the position vector...

    Text Solution

    |

  16. If a, b and c are three non-zero vectors such that each one of them be...

    Text Solution

    |

  17. Let a=hat(i)+hat(j)+hat(k), b=hat(i)-hat(j)+hat(k) and c=hat(i)-hat(j)...

    Text Solution

    |

  18. If r a=r. b=r. c=1 where a, b, c are any three non-coplanar vectors, t...

    Text Solution

    |

  19. If |a|=3 and -1 le k le 2, then |k a|lies in the interval

    Text Solution

    |

  20. If ABCDEF is regular hexagon, then AD+EB+FC is equal to

    Text Solution

    |