Home
Class 12
MATHS
If vec a , vec b , vec ca n d vec d are...

If ` vec a , vec b , vec ca n d vec d` are four vectors in three-dimensional space with the same initial point and such that `3 vec a-2 vec b+ vec c-2 vec d=0` , show that terminals `A ,B ,Ca n d D` of these vectors are coplanar. Find the point at which `A Ca n dB D` meet. Find the ratio in which `P` divides `A Ca n dB Ddot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If vec a , vec b , vec ca n d vec d are four vectors in three-dimensional space with the same initial point and such that 3 vec a+2 vec b+ vec c-2 vec d=0 , Find the point at which A Ca n dB D meet. Find the ratio in which P divides A Ca n dB Ddot

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

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

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

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

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

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is 0 b. 1 c. -sqrt(3) d. sqrt(3)

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 ,\ t h e n\ A B C D is a a. rhombus b. rectangle c. square d. parallelogram

Let vec a\ a n d\ vec b be two vectors of the same magnitude such that the angle between then is 60^0 and vec adot vec b=8. Find | vec a|a n d\ | vec b|dot

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. ABCD  is a quadrilateral and  E  is the point of intersection of ...

    Text Solution

    |

  2. ABCD is a parallelogram. If L and M be the middle points of BC and CD,...

    Text Solution

    |

  3. If vec a , vec b , vec ca n d vec d are four vectors in three-dimensi...

    Text Solution

    |

  4. Find the vector of magnitude 3, bisecting the angle between the vec...

    Text Solution

    |

  5. If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 ...

    Text Solution

    |

  6. If vec r1, vec r2, vec r3 are the position vectors of the collinear ...

    Text Solution

    |

  7. Examine the following vector for linear independence: (1) vec i+ve...

    Text Solution

    |

  8. Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n...

    Text Solution

    |

  9. Let vec a , vec ba n d vec c be three units vectors such that 2 vec a...

    Text Solution

    |

  10. Four non –zero vectors will always be a.  linearly dependent       ...

    Text Solution

    |

  11. A boat moves in still water with a velocity which is k times less t...

    Text Solution

    |

  12. In a triangle P Q R ,Sa n dT are points on Q Ra n dP R , respectively,...

    Text Solution

    |

  13. In a quadrilateral P Q R S , vec P Q= vec a , vec Q R = vec b , vec S ...

    Text Solution

    |

  14. solve the differential equation (1+x^2)dy/dx=x

    Text Solution

    |

  15. Sow that x1 hat i+y1 hat j+z1 hat k ,x2 hat i+y2 hat j+z2 hat k ,a n d...

    Text Solution

    |

  16. The position vector of the points P and Q are 5 hat i+7 hat j-2 hat ...

    Text Solution

    |

  17. Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat...

    Text Solution

    |

  18. If vec a and vec b are two unit vectors and theta is the angle between...

    Text Solution

    |

  19. The vectors x hat i+(x+1) hat j+(x+2) hat k ,(x+3) hat i+(x+4) hat j+(...

    Text Solution

    |

  20. vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammad...

    Text Solution

    |