Home
Class 12
MATHS
The position vectors of the vertices ...

The position vectors of the vertices `A ,Ba n dC` of a triangle are three unit vectors ` vec a , vec b ,a n d vec c ,` respectively. A vector ` vec d` is such that ` vec ddot vec a= vec ddot vec ba n d vec d=lambda( vec b+ vec c)dot` Then triangle `A B C` is a. acute angled b. obtuse angled c. right angled d. none of these

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

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vecd dot vec a= vecd dot vec b= vec d dot vec ca n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

If vec a , vec b , vec c are three non coplanar vectors such that vec adot vec a= vec d vec b= vec ddot vec c=0 , then show that vec d is the null vector.

If vec a ,\ vec b ,\ vec c are three vectors such that vec adot vec b= vec adot vec c then show that vec a=0\ or ,\ vec b=c\ or\ vec a_|_( vec b- vec c)dot

If vec a ,\ vec b ,\ vec c are three non coplanar vectors such that vec d dot vec a= vec d dot vec b= vec d dot vec c=0, then show that d is the null vector.

Find the angle between two vectors vec a\ a n d\ vec b , if | vec axx vec b|= vec adot vec bdot

Let vec a , vec b , vec c be unit vectors such that vec adot vec b= vec adot vec c=0 and the angle between vec ba n d vec c is pi/6,t h a t vec a=+-2( vec bxx vec c)dot

Prove that the points A ,Ba n d C with position vectors vec a , vec ba n d vec c respectively are collinear if and only if vec axx vec b+ vec bxx vec c+ vec cxx vec a= vec0dot

If vec a\ a n d\ vec b are two vectors such that | vec a|=| vec axx vec b|, write the angle between vec a\ a n d\ vec bdot

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\ a n d\ vec b are two vectors such that | vec axx vec b|=3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ vec b .

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Statement 1: If | vec a+ vec b|=| vec a- vec b|, then vec a and vec b ...

    Text Solution

    |

  2. Statement 1: vec a=3 vec i+p vec j+3 vec k and vec b=2 vec i+3 vec j...

    Text Solution

    |

  3. The position vectors of the vertices A ,Ba n dC of a triangle are t...

    Text Solution

    |

  4. aa n db form the consecutive sides of a regular hexagon A B C D E F...

    Text Solution

    |

  5. Column I, Column II Collinear vectors, p. vec a Coinitial vec...

    Text Solution

    |

  6. Statement 1: | vec a|=3,| vec b|= 4 a n d | vec a+ vec b|=5,t h e n| ...

    Text Solution

    |

  7. A man travelling towards east at 8km/h finds that the wind seems to...

    Text Solution

    |

  8. OABCDE is a regular hexagon of side 2 units in the XY-plane in the ...

    Text Solution

    |

  9. If vec a=7 hat i-4 hat j-4 hat k and vec b=-2 hat i- hat j+2 hat k , ...

    Text Solution

    |

  10. Find a unit vector vec c if vec -i+vec j-vec k bisects the angle betw...

    Text Solution

    |

  11. The vectors 2i+3 hat j ,5 hat i+6 hat j and 8 hat i+lambda hat j have ...

    Text Solution

    |

  12. If vec a , vec b and vec c are three non-zero vectors, no two of whic...

    Text Solution

    |

  13. i. Prove that the points vec a-2vec b+3vec c, 2vec a+3vec b-4vec ...

    Text Solution

    |

  14. Check whether the given three vectors are coplanar or non-coplanar. -2...

    Text Solution

    |

  15. Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ...

    Text Solution

    |

  16. If vec a and vec b are two non-collinear vectors, show that points l1...

    Text Solution

    |

  17. Show, by vector methods, that the angularbisectors of a triangle are c...

    Text Solution

    |

  18. Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...

    Text Solution

    |

  19. Find the least positive integral value of x for which the angle betwee...

    Text Solution

    |

  20. If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat k ...

    Text Solution

    |