Home
Class 12
MATHS
If vec a ,\ vec b ,\ vec c are the po...

If ` vec a ,\ vec b ,\ vec c` are the position vectors of the vertices of an equilateral triangle whose orthocentre is t the origin, then write the value of ` vec a+ vec b+ vec cdot`

A

`vec a + vec b + vec c = vec 0`

B

`|vec a|^(2)=|vec b|^(2) + |vec c|^(2)`

C

`vec a + vec b = vec c `

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • ALGEBRA OF VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • ALGEBRAIC INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|39 Videos

Similar Questions

Explore conceptually related problems

If vec a ,\ vec b ,\ vec c are the position vectors of the vertices of an equilateral triangle whose orthocentre is the origin, then write the value of vec a+ vec b+ vec c

If vec a ,\ vec b ,\ vec c are position vectors of the vertices of a triangle, then write the position vector of its centroid.

If vec a ,\ vec b ,\ vec c are position vectors of the vertices A ,\ B\ a n d\ C respectively, of a triangle A B C ,\ write the value of vec A B+ vec B C+ vec C Adot

If vec a , vec b , vec ca n d vec d are the position vectors of the vertices of a cyclic quadrilateral A B C D , prove that (| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/(( vec b- vec a)dot( vec d- vec a))+(| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/(( vec b- vec c)dot( vec d- vec c))=0dot

If vec a ,\ vec b ,\ vec c\ represent the sides of a triangle taken in order, then write the value of vec a+ vec b+ vec c

If vec a , vec b , vec c are unit vectors such that vec a. vec b=0= vec a. vec c and the angle between vec b and vec c is pi/3, then find the value of | vec axx vec b- vec axx vec c| .

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

If vec(a), vec(b), vec(c) are the position vectors of vertices A, B, C of a triangle ABC, Show that the area of the triangle is (1)/(2) |vec(b) xx vec(c) + vec(c) xx vec(a) + vec(a) xx vec(b)|

If vec a\ a n d\ vec b are vectors of equal magnitude, write the value of ( vec a+ vec b)dot( vec a- vec b)dot

OBJECTIVE RD SHARMA ENGLISH-ALGEBRA OF VECTORS-Exercise
  1. If veca is a non-zero vector of modulus a and m is a non-zero scalar, ...

    Text Solution

    |

  2. D, E and F are the mid-points of the sides BC, CA and AB respectively ...

    Text Solution

    |

  3. If vec a ,\ vec b ,\ vec c are the position vectors of the vertices...

    Text Solution

    |

  4. If P, Q, R are three points with respective position vectors hati + ha...

    Text Solution

    |

  5. Let ABC be a triangle, the position vectors of whose vertices are 7hat...

    Text Solution

    |

  6. If vec a = hati + 2 hatj + 2 hat k and vec b = 3 hati + 6 hatj + 2 h...

    Text Solution

    |

  7. veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b ...

    Text Solution

    |

  8. The vector vec c , directed along the internal bisector of the angle...

    Text Solution

    |

  9. A, B have vectors vec a , vec b relative to the origin O and X, Y d...

    Text Solution

    |

  10. If a vector ofmagnitude 50 is collinear with vector vecb = 6 hat i - 8...

    Text Solution

    |

  11. The vector vec c , directed along the internal bisector of the angle...

    Text Solution

    |

  12. Let vec a , vec b ,vec c are three non- coplanar vectors such that ...

    Text Solution

    |

  13. If vec a, vec b , vec c are three non- coplanar vectors such that v...

    Text Solution

    |

  14. veca, vecb ,vecc are three non zero vectors no two of which are collon...

    Text Solution

    |

  15. Let alpha,beta and gamma be distinct real numbers. The points with pos...

    Text Solution

    |

  16. The points with position vectors 60hati+3hatj,40hati-8hatj, ahati-52ha...

    Text Solution

    |

  17. If the points with position vectors 10 hat i+3 hat j ,12 hat i-5 ha...

    Text Solution

    |

  18. If C is the middle point of AB and P is any point outside AB, then

    Text Solution

    |

  19. The median AD of the DeltaABC is bisected at E.BE meets AC in F. then,...

    Text Solution

    |

  20. In a trapezium, the vector BC=lamdaAD. We will then find that p=AC+BD ...

    Text Solution

    |