Home
Class 12
MATHS
Statement -1 If xbara+ybarb+zbarc=0 impl...

Statement -1 If `xbara+ybarb+zbarc=0 implies x+y+z=0` where x,y,z are scalars and `bara,barb,barc` are p.v of three points A,B,C then A,B,C are linearly dependent.
Statement-2: A,B,C are collinear points.

A

Statement -1 is true, Statement -2 is true, Statement-2 is a correct explanation for Statement -1

B

Statement-1 is true,Statement-2 is true,Statement-2is NOT a correct explanation for Statement-1

C

Statement-1 is True,Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • VECTOR

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|18 Videos

  • VECTOR

    FIITJEE|Exercise COMPREHENSIONS|3 Videos

  • VECTOR

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) LEVEL-II|6 Videos

  • TRIGONOMETIC EQUATIONS

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

If bara,barb are non-collinear vectors and x,y are scalars such that xbara+ybarb=bar0 , then

If bara,barb,barc are non-collinear vectors such that for some scalar x,y,z,xbara+ybarb+zbarc=0 , then

a,b and c are in A.P.and x, y,z are in G.P.The points (a,x),(b,y) and (C,z) are collinear if

If the position vectors of the points A,B,C are bara,barb and 3bara-2barb respectively, then the position A,B,C are

If bara,barb are non-collinear vectors and x,y are scalars such that (1bara-barb)x+(2barb-bara)y+(bara+2barb)=bar0 , then

If bara,barb,barc are non-coplanar vectors and x, y, z are scalars such that bara = x (barb xx barc) + y (barc xx bara) + z (bara xx barb) , then x =

If the points A(x,y+z),B(y,z+x) and "C(z,x+y)" are such that AB=BC ,then x,y,z are in A .P

Statement 1: If the lines 2x+3y+19=0 and 9x+6y-17=0 cut the x -axis at A,B and the y-axis at C,D, then the points,A,B,C,D are concyclic.Statement 2: since OAxOB=OCxOD, where O is the origin,A,B,C,D are concyclic.

FIITJEE-VECTOR-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. IF a,b,c are three real numbers not all equal and the vectors barx=aha...

    Text Solution

    |

  2. Consider triangleABC and triangleA1B1C1 in such a way that bar(AB)=ba...

    Text Solution

    |

  3. Let bara=hati+hatj+hatk,barb=x1hati+x2hatj+x3hatk where x1,x2,x3 in (-...

    Text Solution

    |

  4. Let bara and barb be two vectors of equal magnitude 5units. Let barp,q...

    Text Solution

    |

  5. Consider a parallelogram constructed as 5bara+2barb and bara-3barb whe...

    Text Solution

    |

  6. The vectors vecx and vecy satisfy the equation pvecx+qvecy=veca (where...

    Text Solution

    |

  7. Let bara and barb be two non coplanar unit vectors IF baru=bara-(bara....

    Text Solution

    |

  8. A vector bara has components a1,a2,a3 in the right handed rectangular ...

    Text Solution

    |

  9. Let DeltaABC be given triangle IF |barBA+tbarBC |ge |barAC| for any t ...

    Text Solution

    |

  10. If barr.bara=barr.barb=barr.barc=0 for non-zero vector barr then the v...

    Text Solution

    |

  11. vecr=3hati+2hatj-5hatk, veca=2hati-hatj+hatk, vecb=hati+3hatj-2hatk, v...

    Text Solution

    |

  12. Let bara barb barc be three unit vectors such that |bara+barb+barc|=1 ...

    Text Solution

    |

  13. IF bara=hati+hatj+hatk,barb=2hatj-hatk and barr times bara=barb times ...

    Text Solution

    |

  14. The vector has components 2p and 1 with respect to a rectangular Carte...

    Text Solution

    |

  15. Let bara be a unit vector perpendicular to unit vectors barb and barc ...

    Text Solution

    |

  16. A non-zero vector bara is parallel to the line of intersection of the ...

    Text Solution

    |

  17. phati+3hatj+4hatk and sqrt(q)i+4hatk are two vectors, where p,q ge 0 a...

    Text Solution

    |

  18. Statement -1 If xbara+ybarb+zbarc=0 implies x+y+z=0 where x,y,z are sc...

    Text Solution

    |

  19. Statement-1 Let three are 2010 vectors in a plane such that sum of eve...

    Text Solution

    |

  20. Statement-1 Unit vector Orthogonal to 5hati+2hatj+6hatk are coplanar w...

    Text Solution

    |