Home
Class 12
MATHS
If vec a ,vec b,vec c and vec d are the...

If `vec a ,vec b,vec c and vec d` are the position vectors of the points A, B, C and D respectively in three dimensionalspace no three of A, B, C, D are collinear and satisfy the relation `3vec a-2vec b +vec c-2vec d = 0` , then

A

A, B, C and D are coplanar

B

The line joining the points B and D divides the line joining the point A and C in the ratio of `2:1`

C

The line joining the points A and C divides the line joining the points B and D in the ratio of `1:1`

D

The four vectors `veca, vecb, vec c and vecd` are linearly dependent .

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Promotional Banner

Topper's Solved these Questions

  • VECTOR & 3DIMENSIONAL GEOMETRY

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-3 : Comprehension Type Problems|18 Videos

  • VECTOR & 3DIMENSIONAL GEOMETRY

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-4 : Matching Type Problems|1 Videos

  • VECTOR & 3DIMENSIONAL GEOMETRY

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|18 Videos

  • TRIGONOMETRIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|9 Videos

Similar Questions

Explore conceptually related problems

If vec a , vec b , vec c and vec d are the position vectors of points A, B, C, D such that no three of them are collinear and vec a + vec c = vec b + vec d , then ABCD is a

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.

If vec(b) and vec(c ) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD)= 4 vec(BC) is

vec a,vec b,vec c,vec d are the position vectors of the four distinct points A,B,C, D respectively.If vec b-vec a=vec c-vec d, then show that ABCD is a parallelogram.

If vec(b) and vec(c) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD) = 4 vec(BC) is

If vec a,vec b,vec c are the position vectors of points A,B,C and D respectively such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 then D is the

If vec a,vec b,vec c and vec d are the position vectors of points A,B,C,D such that no three of them are collinear and vec a+vec c=vec b+vec d, then ABCD is a a. rhombus b.rectangle c.square d. parallelogram

Let vec a,vec b,vec c,vec d be the position vectors of the four distinct points A,B,C,D. If vec b-vec a=vec a-vec d, then show that ABCD is parallelogram.

Show that the four points A,B,C and D with position vectors vec a,vec b,vec c and vec d respectively are coplanar if and only if 3vec a-2vec b+vec c-2vec d=0

VIKAS GUPTA (BLACK BOOK)-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-2 : One or More than One Answer is/are Correct
  1. If veca=hati+6hatj+3hatk;vecb=3hati+2hatj+hatk and vec c=(alpha+1)hati...

    Text Solution

    |

  2. Consider the lines: L1:(x-2)/1=(y-1)/7=(z+2)/-5, L2:x-4=y+3=-z Then wh...

    Text Solution

    |

  3. Let hata, hatb and hatc be three unit vectors such that hata=hatb+(h...

    Text Solution

    |

  4. The value(s) of mu for which the straight lines vecr=3hati-2hatj-4hatk...

    Text Solution

    |

  5. If hati xx[(veca-hatj)xxhati]xx[(veca-hatk)xxhatj]+veckxx[(veca-veci)x...

    Text Solution

    |

  6. The value of expression [veca xx vecb" "vec c xx vecd" " vece xx vecf...

    Text Solution

    |

  7. If vec a ,vec b,vec c and vec d are the position vectors of the point...

    Text Solution

    |

  8. If OAB is a tetrahedron with edges and hatp, hatq, hatr are unit vect...

    Text Solution

    |

  9. Let hata and hatc are unit vectors and |vecb|=4. If the angle between...

    Text Solution

    |

  10. Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2, then

    Text Solution

    |

  11. Let vecr=sinx (veca xx vecb)+cosy(vecb xx vec c)+2(vec c xx veca), whe...

    Text Solution

    |

  12. If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd, wh...

    Text Solution

    |

  13. Let a be a real number and vec alpha = hati +2hatj, vec beta=2hati+a h...

    Text Solution

    |

  14. The volume of a tetrahedron prism ABCA1B1C1 is equal to 3. Find the co...

    Text Solution

    |

  15. If veca=x hati+y hatj+z hatk, vecb=y hati+z hatj+x hatk, and vec c=z ...

    Text Solution

    |

  16. If a line has a vector equation, vecr=2hati +6hatj+lambda(hati-3hatj) ...

    Text Solution

    |

  17. Let M,N, P and Q be the mid points of the edges AB, CD, AC and BD resp...

    Text Solution

    |

  18. The solution vectors vecr of the equation vecr xx hati=hatj+hatk and v...

    Text Solution

    |

  19. Which of the following statement(s) is/are incorrect ?

    Text Solution

    |

  20. The lines with vector equations are, vecr(1)=3hati+6hatj+lambda(-4hat...

    Text Solution

    |